id	topic_id	thread_id	type	formula
q_253	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""p\to q"" class=""ltx_Math"" display=""block"" id=""S0.Ex1.m1.1""><apply id=""S0.Ex1.m1.1.4"" xref=""S0.Ex1.m1.1.4.pmml""><ci id=""S0.Ex1.m1.1.2"" xref=""S0.Ex1.m1.1.2.pmml"">→</ci><ci id=""S0.Ex1.m1.1.1"" xref=""S0.Ex1.m1.1.1.pmml"">p</ci><ci id=""S0.Ex1.m1.1.3"" xref=""S0.Ex1.m1.1.3.pmml"">q</ci></apply></math>"
q_254	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""p"" class=""ltx_Math"" display=""block"" id=""S0.Ex2.m1.1""><ci id=""S0.Ex2.m1.1.1"" xref=""S0.Ex2.m1.1.1.pmml"">p</ci></math>"
q_255	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""q"" class=""ltx_Math"" display=""block"" id=""S0.Ex3.m1.1""><ci id=""S0.Ex3.m1.1.1"" xref=""S0.Ex3.m1.1.1.pmml"">q</ci></math>"
q_256	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""p\to q"" class=""ltx_Math"" display=""block"" id=""S0.Ex4.m1.1""><apply id=""S0.Ex4.m1.1.4"" xref=""S0.Ex4.m1.1.4.pmml""><ci id=""S0.Ex4.m1.1.2"" xref=""S0.Ex4.m1.1.2.pmml"">→</ci><ci id=""S0.Ex4.m1.1.1"" xref=""S0.Ex4.m1.1.1.pmml"">p</ci><ci id=""S0.Ex4.m1.1.3"" xref=""S0.Ex4.m1.1.3.pmml"">q</ci></apply></math>"
q_257	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""p"" class=""ltx_Math"" display=""block"" id=""S0.Ex5.m1.1""><ci id=""S0.Ex5.m1.1.1"" xref=""S0.Ex5.m1.1.1.pmml"">p</ci></math>"
q_258	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""q"" class=""ltx_Math"" display=""block"" id=""S0.Ex6.m1.1""><ci id=""S0.Ex6.m1.1.1"" xref=""S0.Ex6.m1.1.1.pmml"">q</ci></math>"
q_259	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""p"" class=""ltx_Math"" display=""block"" id=""S0.Ex7.m1.1""><ci id=""S0.Ex7.m1.1.1"" xref=""S0.Ex7.m1.1.1.pmml"">p</ci></math>"
q_260	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""q"" class=""ltx_Math"" display=""block"" id=""S0.Ex8.m1.1""><ci id=""S0.Ex8.m1.1.1"" xref=""S0.Ex8.m1.1.1.pmml"">q</ci></math>"
q_261	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""p\to q"" class=""ltx_Math"" display=""block"" id=""S0.Ex9.m1.1""><apply id=""S0.Ex9.m1.1.4"" xref=""S0.Ex9.m1.1.4.pmml""><ci id=""S0.Ex9.m1.1.2"" xref=""S0.Ex9.m1.1.2.pmml"">→</ci><ci id=""S0.Ex9.m1.1.1"" xref=""S0.Ex9.m1.1.1.pmml"">p</ci><ci id=""S0.Ex9.m1.1.3"" xref=""S0.Ex9.m1.1.3.pmml"">q</ci></apply></math>"
q_730	A.78	3237032	title	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""\sum_{n=1}^{\infty}a_{n}"" class=""ltx_Math"" display=""block"" id=""S0.Ex10.m1.1""><apply id=""S0.Ex10.m1.1.6"" xref=""S0.Ex10.m1.1.6.pmml""><apply id=""S0.Ex10.m1.1.6.1"" xref=""S0.Ex10.m1.1.6.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex10.m1.1.6.1.1"" xref=""S0.Ex10.m1.1.6.1.pmml"">superscript</csymbol><apply id=""S0.Ex10.m1.1.6.1.2"" xref=""S0.Ex10.m1.1.6.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex10.m1.1.6.1.2.1"" xref=""S0.Ex10.m1.1.6.1.pmml"">subscript</csymbol><sum id=""S0.Ex10.m1.1.1"" xref=""S0.Ex10.m1.1.1.pmml""/><apply id=""S0.Ex10.m1.1.2.1"" xref=""S0.Ex10.m1.1.2.1.pmml""><eq id=""S0.Ex10.m1.1.2.1.2"" xref=""S0.Ex10.m1.1.2.1.2.pmml""/><ci id=""S0.Ex10.m1.1.2.1.1"" xref=""S0.Ex10.m1.1.2.1.1.pmml"">n</ci><cn id=""S0.Ex10.m1.1.2.1.3"" type=""integer"" xref=""S0.Ex10.m1.1.2.1.3.pmml"">1</cn></apply></apply><infinity id=""S0.Ex10.m1.1.3.1"" xref=""S0.Ex10.m1.1.3.1.pmml""/></apply><apply id=""S0.Ex10.m1.1.6.2"" xref=""S0.Ex10.m1.1.6.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex10.m1.1.6.2.1"" xref=""S0.Ex10.m1.1.6.2.pmml"">subscript</csymbol><ci id=""S0.Ex10.m1.1.4"" xref=""S0.Ex10.m1.1.4.pmml"">a</ci><ci id=""S0.Ex10.m1.1.5.1"" xref=""S0.Ex10.m1.1.5.1.pmml"">n</ci></apply></apply></math>"
q_731	A.78	3237032	title	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""\sum_{n=1}^{\infty}a_{n}^{2}"" class=""ltx_Math"" display=""block"" id=""S0.Ex11.m1.1""><apply id=""S0.Ex11.m1.1.7"" xref=""S0.Ex11.m1.1.7.pmml""><apply id=""S0.Ex11.m1.1.7.1"" xref=""S0.Ex11.m1.1.7.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex11.m1.1.7.1.1"" xref=""S0.Ex11.m1.1.7.1.pmml"">superscript</csymbol><apply id=""S0.Ex11.m1.1.7.1.2"" xref=""S0.Ex11.m1.1.7.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex11.m1.1.7.1.2.1"" xref=""S0.Ex11.m1.1.7.1.pmml"">subscript</csymbol><sum id=""S0.Ex11.m1.1.1"" xref=""S0.Ex11.m1.1.1.pmml""/><apply id=""S0.Ex11.m1.1.2.1"" xref=""S0.Ex11.m1.1.2.1.pmml""><eq id=""S0.Ex11.m1.1.2.1.2"" xref=""S0.Ex11.m1.1.2.1.2.pmml""/><ci id=""S0.Ex11.m1.1.2.1.1"" xref=""S0.Ex11.m1.1.2.1.1.pmml"">n</ci><cn id=""S0.Ex11.m1.1.2.1.3"" type=""integer"" xref=""S0.Ex11.m1.1.2.1.3.pmml"">1</cn></apply></apply><infinity id=""S0.Ex11.m1.1.3.1"" xref=""S0.Ex11.m1.1.3.1.pmml""/></apply><apply id=""S0.Ex11.m1.1.7.2"" xref=""S0.Ex11.m1.1.7.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex11.m1.1.7.2.1"" xref=""S0.Ex11.m1.1.7.2.pmml"">superscript</csymbol><apply id=""S0.Ex11.m1.1.7.2.2"" xref=""S0.Ex11.m1.1.7.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex11.m1.1.7.2.2.1"" xref=""S0.Ex11.m1.1.7.2.pmml"">subscript</csymbol><ci id=""S0.Ex11.m1.1.4"" xref=""S0.Ex11.m1.1.4.pmml"">a</ci><ci id=""S0.Ex11.m1.1.5.1"" xref=""S0.Ex11.m1.1.5.1.pmml"">n</ci></apply><cn id=""S0.Ex11.m1.1.6.1"" type=""integer"" xref=""S0.Ex11.m1.1.6.1.pmml"">2</cn></apply></apply></math>"
q_732	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""\epsilon&amp;gt;0"" class=""ltx_Math"" display=""block"" id=""S0.Ex12.m1.1""><list id=""S0.Ex12.m1.1.7.1"" xref=""S0.Ex12.m1.1.7.pmml""><apply id=""S0.Ex12.m1.1.7.2"" xref=""S0.Ex12.m1.1.7.2.pmml""><times id=""S0.Ex12.m1.1.7.2.1"" xref=""S0.Ex12.m1.1.7.2.1.pmml""/><ci id=""S0.Ex12.m1.1.1"" xref=""S0.Ex12.m1.1.1.pmml"">italic-ε</ci><ci id=""S0.Ex12.m1.1.2"" xref=""S0.Ex12.m1.1.2.pmml"">&amp;</ci><ci id=""S0.Ex12.m1.1.3"" xref=""S0.Ex12.m1.1.3.pmml"">g</ci><ci id=""S0.Ex12.m1.1.4"" xref=""S0.Ex12.m1.1.4.pmml"">t</ci></apply><cn id=""S0.Ex12.m1.1.6"" type=""integer"" xref=""S0.Ex12.m1.1.6.pmml"">0</cn></list></math>"
q_733	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""\sum a_{n}"" class=""ltx_Math"" display=""block"" id=""S0.Ex13.m1.1""><apply id=""S0.Ex13.m1.1.4"" xref=""S0.Ex13.m1.1.4.pmml""><sum id=""S0.Ex13.m1.1.1"" xref=""S0.Ex13.m1.1.1.pmml""/><apply id=""S0.Ex13.m1.1.4.1"" xref=""S0.Ex13.m1.1.4.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex13.m1.1.4.1.1"" xref=""S0.Ex13.m1.1.4.1.pmml"">subscript</csymbol><ci id=""S0.Ex13.m1.1.2"" xref=""S0.Ex13.m1.1.2.pmml"">a</ci><ci id=""S0.Ex13.m1.1.3.1"" xref=""S0.Ex13.m1.1.3.1.pmml"">n</ci></apply></apply></math>"
q_734	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""n&amp;gt;m\geq N"" class=""ltx_Math"" display=""block"" id=""S0.Ex14.m1.1""><apply id=""S0.Ex14.m1.1.9"" xref=""S0.Ex14.m1.1.9.pmml""><geq id=""S0.Ex14.m1.1.7"" xref=""S0.Ex14.m1.1.7.pmml""/><list id=""S0.Ex14.m1.1.9.1.1"" xref=""S0.Ex14.m1.1.9.1.pmml""><apply id=""S0.Ex14.m1.1.9.1.2"" xref=""S0.Ex14.m1.1.9.1.2.pmml""><times id=""S0.Ex14.m1.1.9.1.2.1"" xref=""S0.Ex14.m1.1.9.1.2.1.pmml""/><ci id=""S0.Ex14.m1.1.1"" xref=""S0.Ex14.m1.1.1.pmml"">n</ci><ci id=""S0.Ex14.m1.1.2"" xref=""S0.Ex14.m1.1.2.pmml"">&amp;</ci><ci id=""S0.Ex14.m1.1.3"" xref=""S0.Ex14.m1.1.3.pmml"">g</ci><ci id=""S0.Ex14.m1.1.4"" xref=""S0.Ex14.m1.1.4.pmml"">t</ci></apply><ci id=""S0.Ex14.m1.1.6"" xref=""S0.Ex14.m1.1.6.pmml"">m</ci></list><ci id=""S0.Ex14.m1.1.8"" xref=""S0.Ex14.m1.1.8.pmml"">N</ci></apply></math>"
q_735	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""|\sum_{k=m+1}^{n}|a_{k}||=\sum_{k=m+1}^{n}|a_{k}|&amp;lt;\sqrt{\epsilon}"" class=""ltx_Math"" display=""block"" id=""S0.Ex15.m1.1""><apply id=""S0.Ex15.m1.1.23"" xref=""S0.Ex15.m1.1.23.pmml""><eq id=""S0.Ex15.m1.1.10"" xref=""S0.Ex15.m1.1.10.pmml""/><apply id=""S0.Ex15.m1.1.23.1.1"" xref=""S0.Ex15.m1.1.23.1.pmml""><abs id=""S0.Ex15.m1.1.23.1.1.1"" xref=""S0.Ex15.m1.1.1.pmml""/><apply id=""S0.Ex15.m1.1.23.1.2"" xref=""S0.Ex15.m1.1.23.1.2.pmml""><apply id=""S0.Ex15.m1.1.23.1.2.1"" xref=""S0.Ex15.m1.1.23.1.2.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex15.m1.1.23.1.2.1.1"" xref=""S0.Ex15.m1.1.23.1.2.1.pmml"">superscript</csymbol><apply id=""S0.Ex15.m1.1.23.1.2.1.2"" xref=""S0.Ex15.m1.1.23.1.2.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex15.m1.1.23.1.2.1.2.1"" xref=""S0.Ex15.m1.1.23.1.2.1.pmml"">subscript</csymbol><sum id=""S0.Ex15.m1.1.2"" xref=""S0.Ex15.m1.1.2.pmml""/><apply id=""S0.Ex15.m1.1.3.1"" xref=""S0.Ex15.m1.1.3.1.pmml""><eq id=""S0.Ex15.m1.1.3.1.2"" xref=""S0.Ex15.m1.1.3.1.2.pmml""/><ci id=""S0.Ex15.m1.1.3.1.1"" xref=""S0.Ex15.m1.1.3.1.1.pmml"">k</ci><apply id=""S0.Ex15.m1.1.3.1.6"" xref=""S0.Ex15.m1.1.3.1.6.pmml""><plus id=""S0.Ex15.m1.1.3.1.4"" xref=""S0.Ex15.m1.1.3.1.4.pmml""/><ci id=""S0.Ex15.m1.1.3.1.3"" xref=""S0.Ex15.m1.1.3.1.3.pmml"">m</ci><cn id=""S0.Ex15.m1.1.3.1.5"" type=""integer"" xref=""S0.Ex15.m1.1.3.1.5.pmml"">1</cn></apply></apply></apply><ci id=""S0.Ex15.m1.1.4.1"" xref=""S0.Ex15.m1.1.4.1.pmml"">n</ci></apply><apply id=""S0.Ex15.m1.1.23.1.2.2.1"" xref=""S0.Ex15.m1.1.23.1.2.2.pmml""><abs id=""S0.Ex15.m1.1.23.1.2.2.1.1"" xref=""S0.Ex15.m1.1.5.pmml""/><apply id=""S0.Ex15.m1.1.23.1.2.2.2"" xref=""S0.Ex15.m1.1.23.1.2.2.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex15.m1.1.23.1.2.2.2.1"" xref=""S0.Ex15.m1.1.23.1.2.2.2.pmml"">subscript</csymbol><ci id=""S0.Ex15.m1.1.6"" xref=""S0.Ex15.m1.1.6.pmml"">a</ci><ci id=""S0.Ex15.m1.1.7.1"" xref=""S0.Ex15.m1.1.7.1.pmml"">k</ci></apply></apply></apply></apply><list id=""S0.Ex15.m1.1.23.2.1"" xref=""S0.Ex15.m1.1.23.2.pmml""><apply id=""S0.Ex15.m1.1.23.2.2"" xref=""S0.Ex15.m1.1.23.2.2.pmml""><apply id=""S0.Ex15.m1.1.23.2.2.1"" xref=""S0.Ex15.m1.1.23.2.2.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex15.m1.1.23.2.2.1.1"" xref=""S0.Ex15.m1.1.23.2.2.1.pmml"">superscript</csymbol><apply id=""S0.Ex15.m1.1.23.2.2.1.2"" xref=""S0.Ex15.m1.1.23.2.2.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex15.m1.1.23.2.2.1.2.1"" xref=""S0.Ex15.m1.1.23.2.2.1.pmml"">subscript</csymbol><sum id=""S0.Ex15.m1.1.11"" xref=""S0.Ex15.m1.1.11.pmml""/><apply id=""S0.Ex15.m1.1.12.1"" xref=""S0.Ex15.m1.1.12.1.pmml""><eq id=""S0.Ex15.m1.1.12.1.2"" xref=""S0.Ex15.m1.1.12.1.2.pmml""/><ci id=""S0.Ex15.m1.1.12.1.1"" xref=""S0.Ex15.m1.1.12.1.1.pmml"">k</ci><apply id=""S0.Ex15.m1.1.12.1.6"" xref=""S0.Ex15.m1.1.12.1.6.pmml""><plus id=""S0.Ex15.m1.1.12.1.4"" xref=""S0.Ex15.m1.1.12.1.4.pmml""/><ci id=""S0.Ex15.m1.1.12.1.3"" xref=""S0.Ex15.m1.1.12.1.3.pmml"">m</ci><cn id=""S0.Ex15.m1.1.12.1.5"" type=""integer"" xref=""S0.Ex15.m1.1.12.1.5.pmml"">1</cn></apply></apply></apply><ci id=""S0.Ex15.m1.1.13.1"" xref=""S0.Ex15.m1.1.13.1.pmml"">n</ci></apply><apply id=""S0.Ex15.m1.1.23.2.2.2"" xref=""S0.Ex15.m1.1.23.2.2.2.pmml""><times id=""S0.Ex15.m1.1.23.2.2.2.1"" xref=""S0.Ex15.m1.1.23.2.2.2.1.pmml""/><apply id=""S0.Ex15.m1.1.23.2.2.2.2.1"" xref=""S0.Ex15.m1.1.23.2.2.2.2.pmml""><abs id=""S0.Ex15.m1.1.23.2.2.2.2.1.1"" xref=""S0.Ex15.m1.1.14.pmml""/><apply id=""S0.Ex15.m1.1.23.2.2.2.2.2"" xref=""S0.Ex15.m1.1.23.2.2.2.2.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex15.m1.1.23.2.2.2.2.2.1"" xref=""S0.Ex15.m1.1.23.2.2.2.2.2.pmml"">subscript</csymbol><ci id=""S0.Ex15.m1.1.15"" xref=""S0.Ex15.m1.1.15.pmml"">a</ci><ci id=""S0.Ex15.m1.1.16.1"" xref=""S0.Ex15.m1.1.16.1.pmml"">k</ci></apply></apply><ci id=""S0.Ex15.m1.1.18"" xref=""S0.Ex15.m1.1.18.pmml"">&amp;</ci><ci id=""S0.Ex15.m1.1.19"" xref=""S0.Ex15.m1.1.19.pmml"">l</ci><ci id=""S0.Ex15.m1.1.20"" xref=""S0.Ex15.m1.1.20.pmml"">t</ci></apply></apply><apply id=""S0.Ex15.m1.1.22"" xref=""S0.Ex15.m1.1.22.pmml""><root id=""S0.Ex15.m1.1.22a"" xref=""S0.Ex15.m1.1.22.pmml""/><ci id=""S0.Ex15.m1.1.22.2"" xref=""S0.Ex15.m1.1.22.2.pmml"">italic-ε</ci></apply></list></apply></math>"
q_736	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""n&amp;gt;m\geq N"" class=""ltx_Math"" display=""block"" id=""S0.Ex16.m1.1""><apply id=""S0.Ex16.m1.1.9"" xref=""S0.Ex16.m1.1.9.pmml""><geq id=""S0.Ex16.m1.1.7"" xref=""S0.Ex16.m1.1.7.pmml""/><list id=""S0.Ex16.m1.1.9.1.1"" xref=""S0.Ex16.m1.1.9.1.pmml""><apply id=""S0.Ex16.m1.1.9.1.2"" xref=""S0.Ex16.m1.1.9.1.2.pmml""><times id=""S0.Ex16.m1.1.9.1.2.1"" xref=""S0.Ex16.m1.1.9.1.2.1.pmml""/><ci id=""S0.Ex16.m1.1.1"" xref=""S0.Ex16.m1.1.1.pmml"">n</ci><ci id=""S0.Ex16.m1.1.2"" xref=""S0.Ex16.m1.1.2.pmml"">&amp;</ci><ci id=""S0.Ex16.m1.1.3"" xref=""S0.Ex16.m1.1.3.pmml"">g</ci><ci id=""S0.Ex16.m1.1.4"" xref=""S0.Ex16.m1.1.4.pmml"">t</ci></apply><ci id=""S0.Ex16.m1.1.6"" xref=""S0.Ex16.m1.1.6.pmml"">m</ci></list><ci id=""S0.Ex16.m1.1.8"" xref=""S0.Ex16.m1.1.8.pmml"">N</ci></apply></math>"
q_737	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""|\sum_{k=m+1}^{n}a_{k}^{2}|=\sum_{k=m+1}^{n}a_{k}^{2}\leq(\sum_{k=m+1}^{n}|a_{% k}|)^{2}&amp;lt;\sqrt{\epsilon}^{2}=\epsilon"" class=""ltx_Math"" display=""block"" id=""S0.Ex17.m1.1""><apply id=""S0.Ex17.m1.1.35.1"" xref=""S0.Ex17.m1.1.35.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex17.m1.1.35.1a"" xref=""S0.Ex17.m1.1.30.pmml"">formulae-sequence</csymbol><apply id=""S0.Ex17.m1.1.35.2"" xref=""S0.Ex17.m1.1.35.2.pmml""><and id=""S0.Ex17.m1.1.35.2a"" xref=""S0.Ex17.m1.1.35.2.pmml""/><apply id=""S0.Ex17.m1.1.35.2b"" xref=""S0.Ex17.m1.1.35.2.pmml""><eq id=""S0.Ex17.m1.1.9"" xref=""S0.Ex17.m1.1.9.pmml""/><apply id=""S0.Ex17.m1.1.35.2.2.1"" xref=""S0.Ex17.m1.1.35.2.2.pmml""><abs id=""S0.Ex17.m1.1.35.2.2.1.1"" xref=""S0.Ex17.m1.1.1.pmml""/><apply id=""S0.Ex17.m1.1.35.2.2.2"" xref=""S0.Ex17.m1.1.35.2.2.2.pmml""><apply id=""S0.Ex17.m1.1.35.2.2.2.1"" xref=""S0.Ex17.m1.1.35.2.2.2.1.pmml""><csymbol cd=""ambiguous"" 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xref=""S0.Ex17.m1.1.35.2.3.1.pmml"">subscript</csymbol><sum id=""S0.Ex17.m1.1.10"" xref=""S0.Ex17.m1.1.10.pmml""/><apply id=""S0.Ex17.m1.1.11.1"" xref=""S0.Ex17.m1.1.11.1.pmml""><eq id=""S0.Ex17.m1.1.11.1.2"" xref=""S0.Ex17.m1.1.11.1.2.pmml""/><ci id=""S0.Ex17.m1.1.11.1.1"" xref=""S0.Ex17.m1.1.11.1.1.pmml"">k</ci><apply id=""S0.Ex17.m1.1.11.1.6"" xref=""S0.Ex17.m1.1.11.1.6.pmml""><plus id=""S0.Ex17.m1.1.11.1.4"" xref=""S0.Ex17.m1.1.11.1.4.pmml""/><ci id=""S0.Ex17.m1.1.11.1.3"" xref=""S0.Ex17.m1.1.11.1.3.pmml"">m</ci><cn id=""S0.Ex17.m1.1.11.1.5"" type=""integer"" xref=""S0.Ex17.m1.1.11.1.5.pmml"">1</cn></apply></apply></apply><ci id=""S0.Ex17.m1.1.12.1"" xref=""S0.Ex17.m1.1.12.1.pmml"">n</ci></apply><apply id=""S0.Ex17.m1.1.35.2.3.2"" xref=""S0.Ex17.m1.1.35.2.3.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex17.m1.1.35.2.3.2.1"" xref=""S0.Ex17.m1.1.35.2.3.2.pmml"">superscript</csymbol><apply id=""S0.Ex17.m1.1.35.2.3.2.2"" xref=""S0.Ex17.m1.1.35.2.3.2.pmml""><csymbol cd=""ambiguous"" 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xref=""S0.Ex17.m1.1.11.1.pmml""><eq id=""S0.Ex17.m1.1.11.1.2"" xref=""S0.Ex17.m1.1.11.1.2.pmml""/><ci id=""S0.Ex17.m1.1.11.1.1"" xref=""S0.Ex17.m1.1.11.1.1.pmml"">k</ci><apply id=""S0.Ex17.m1.1.11.1.6"" xref=""S0.Ex17.m1.1.11.1.6.pmml""><plus id=""S0.Ex17.m1.1.11.1.4"" xref=""S0.Ex17.m1.1.11.1.4.pmml""/><ci id=""S0.Ex17.m1.1.11.1.3"" xref=""S0.Ex17.m1.1.11.1.3.pmml"">m</ci><cn id=""S0.Ex17.m1.1.11.1.5"" type=""integer"" xref=""S0.Ex17.m1.1.11.1.5.pmml"">1</cn></apply></apply></apply><ci id=""S0.Ex17.m1.1.12.1"" xref=""S0.Ex17.m1.1.12.1.pmml"">n</ci></apply><apply id=""S0.Ex17.m1.1.35.2.3.2"" xref=""S0.Ex17.m1.1.35.2.3.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex17.m1.1.35.2.3.2.1"" xref=""S0.Ex17.m1.1.35.2.3.2.pmml"">superscript</csymbol><apply id=""S0.Ex17.m1.1.35.2.3.2.2"" xref=""S0.Ex17.m1.1.35.2.3.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex17.m1.1.35.2.3.2.2.1"" xref=""S0.Ex17.m1.1.35.2.3.2.pmml"">subscript</csymbol><ci id=""S0.Ex17.m1.1.13"" xref=""S0.Ex17.m1.1.13.pmml"">a</ci><ci id=""S0.Ex17.m1.1.14.1"" xref=""S0.Ex17.m1.1.14.1.pmml"">k</ci></apply><cn id=""S0.Ex17.m1.1.15.1"" type=""integer"" xref=""S0.Ex17.m1.1.15.1.pmml"">2</cn></apply></apply><apply id=""S0.Ex17.m1.1.35.2.4"" xref=""S0.Ex17.m1.1.35.2.4.pmml""><times id=""S0.Ex17.m1.1.35.2.4.1"" xref=""S0.Ex17.m1.1.35.2.4.1.pmml""/><apply id=""S0.Ex17.m1.1.35.2.4.2"" xref=""S0.Ex17.m1.1.35.2.4.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex17.m1.1.35.2.4.2.1"" xref=""S0.Ex17.m1.1.35.2.4.2.pmml"">superscript</csymbol><apply id=""S0.Ex17.m1.1.35.2.4.2.2.2"" xref=""S0.Ex17.m1.1.35.2.4.2.2.pmml""><apply id=""S0.Ex17.m1.1.35.2.4.2.2.2.1"" xref=""S0.Ex17.m1.1.35.2.4.2.2.2.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex17.m1.1.35.2.4.2.2.2.1.1"" xref=""S0.Ex17.m1.1.35.2.4.2.2.2.1.pmml"">superscript</csymbol><apply id=""S0.Ex17.m1.1.35.2.4.2.2.2.1.2"" xref=""S0.Ex17.m1.1.35.2.4.2.2.2.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex17.m1.1.35.2.4.2.2.2.1.2.1"" xref=""S0.Ex17.m1.1.35.2.4.2.2.2.1.pmml"">subscript</csymbol><sum id=""S0.Ex17.m1.1.18"" xref=""S0.Ex17.m1.1.18.pmml""/><apply id=""S0.Ex17.m1.1.19.1"" xref=""S0.Ex17.m1.1.19.1.pmml""><eq id=""S0.Ex17.m1.1.19.1.2"" xref=""S0.Ex17.m1.1.19.1.2.pmml""/><ci id=""S0.Ex17.m1.1.19.1.1"" xref=""S0.Ex17.m1.1.19.1.1.pmml"">k</ci><apply id=""S0.Ex17.m1.1.19.1.6"" xref=""S0.Ex17.m1.1.19.1.6.pmml""><plus id=""S0.Ex17.m1.1.19.1.4"" xref=""S0.Ex17.m1.1.19.1.4.pmml""/><ci id=""S0.Ex17.m1.1.19.1.3"" xref=""S0.Ex17.m1.1.19.1.3.pmml"">m</ci><cn id=""S0.Ex17.m1.1.19.1.5"" type=""integer"" xref=""S0.Ex17.m1.1.19.1.5.pmml"">1</cn></apply></apply></apply><ci id=""S0.Ex17.m1.1.20.1"" xref=""S0.Ex17.m1.1.20.1.pmml"">n</ci></apply><apply id=""S0.Ex17.m1.1.35.2.4.2.2.2.2.1"" xref=""S0.Ex17.m1.1.35.2.4.2.2.2.2.pmml""><abs id=""S0.Ex17.m1.1.35.2.4.2.2.2.2.1.1"" xref=""S0.Ex17.m1.1.21.pmml""/><apply id=""S0.Ex17.m1.1.35.2.4.2.2.2.2.2"" xref=""S0.Ex17.m1.1.35.2.4.2.2.2.2.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex17.m1.1.35.2.4.2.2.2.2.2.1"" xref=""S0.Ex17.m1.1.35.2.4.2.2.2.2.2.pmml"">subscript</csymbol><ci id=""S0.Ex17.m1.1.22"" xref=""S0.Ex17.m1.1.22.pmml"">a</ci><ci id=""S0.Ex17.m1.1.23.1"" xref=""S0.Ex17.m1.1.23.1.pmml"">k</ci></apply></apply></apply><cn id=""S0.Ex17.m1.1.26.1"" type=""integer"" xref=""S0.Ex17.m1.1.26.1.pmml"">2</cn></apply><ci id=""S0.Ex17.m1.1.27"" xref=""S0.Ex17.m1.1.27.pmml"">&amp;</ci><ci id=""S0.Ex17.m1.1.28"" xref=""S0.Ex17.m1.1.28.pmml"">l</ci><ci id=""S0.Ex17.m1.1.29"" xref=""S0.Ex17.m1.1.29.pmml"">t</ci></apply></apply></apply><apply id=""S0.Ex17.m1.1.35.3"" xref=""S0.Ex17.m1.1.35.3.pmml""><eq id=""S0.Ex17.m1.1.33"" xref=""S0.Ex17.m1.1.33.pmml""/><apply id=""S0.Ex17.m1.1.35.3.1"" xref=""S0.Ex17.m1.1.35.3.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex17.m1.1.35.3.1.1"" xref=""S0.Ex17.m1.1.35.3.1.pmml"">superscript</csymbol><apply id=""S0.Ex17.m1.1.31"" xref=""S0.Ex17.m1.1.31.pmml""><root id=""S0.Ex17.m1.1.31a"" xref=""S0.Ex17.m1.1.31.pmml""/><ci id=""S0.Ex17.m1.1.31.2"" xref=""S0.Ex17.m1.1.31.2.pmml"">italic-ε</ci></apply><cn id=""S0.Ex17.m1.1.32.1"" type=""integer"" xref=""S0.Ex17.m1.1.32.1.pmml"">2</cn></apply><ci id=""S0.Ex17.m1.1.34"" xref=""S0.Ex17.m1.1.34.pmml"">italic-ε</ci></apply></apply></math>"
q_738	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""\sum a_{n}^{2}"" class=""ltx_Math"" display=""block"" id=""S0.Ex18.m1.1""><apply id=""S0.Ex18.m1.1.5"" xref=""S0.Ex18.m1.1.5.pmml""><sum id=""S0.Ex18.m1.1.1"" xref=""S0.Ex18.m1.1.1.pmml""/><apply id=""S0.Ex18.m1.1.5.1"" xref=""S0.Ex18.m1.1.5.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex18.m1.1.5.1.1"" xref=""S0.Ex18.m1.1.5.1.pmml"">superscript</csymbol><apply id=""S0.Ex18.m1.1.5.1.2"" xref=""S0.Ex18.m1.1.5.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex18.m1.1.5.1.2.1"" xref=""S0.Ex18.m1.1.5.1.pmml"">subscript</csymbol><ci id=""S0.Ex18.m1.1.2"" xref=""S0.Ex18.m1.1.2.pmml"">a</ci><ci id=""S0.Ex18.m1.1.3.1"" xref=""S0.Ex18.m1.1.3.1.pmml"">n</ci></apply><cn id=""S0.Ex18.m1.1.4.1"" type=""integer"" xref=""S0.Ex18.m1.1.4.1.pmml"">2</cn></apply></apply></math>"
q_1027	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""n^{2}\leq 2^{n}"" class=""ltx_Math"" display=""block"" id=""S0.Ex19.m1.1""><apply id=""S0.Ex19.m1.1.6"" xref=""S0.Ex19.m1.1.6.pmml""><leq id=""S0.Ex19.m1.1.3"" xref=""S0.Ex19.m1.1.3.pmml""/><apply id=""S0.Ex19.m1.1.6.1"" xref=""S0.Ex19.m1.1.6.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex19.m1.1.6.1.1"" xref=""S0.Ex19.m1.1.6.1.pmml"">superscript</csymbol><ci id=""S0.Ex19.m1.1.1"" xref=""S0.Ex19.m1.1.1.pmml"">n</ci><cn id=""S0.Ex19.m1.1.2.1"" type=""integer"" xref=""S0.Ex19.m1.1.2.1.pmml"">2</cn></apply><apply id=""S0.Ex19.m1.1.6.2"" xref=""S0.Ex19.m1.1.6.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex19.m1.1.6.2.1"" xref=""S0.Ex19.m1.1.6.2.pmml"">superscript</csymbol><cn id=""S0.Ex19.m1.1.4"" type=""integer"" xref=""S0.Ex19.m1.1.4.pmml"">2</cn><ci id=""S0.Ex19.m1.1.5.1"" xref=""S0.Ex19.m1.1.5.1.pmml"">n</ci></apply></apply></math>"
q_1028	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""\forall n\in\mathbb{N},n&amp;gt;3"" class=""ltx_Math"" display=""block"" id=""S0.Ex20.m1.1""><apply id=""S0.Ex20.m1.1.12"" xref=""S0.Ex20.m1.1.12.pmml""><in id=""S0.Ex20.m1.1.3"" xref=""S0.Ex20.m1.1.3.pmml""/><apply id=""S0.Ex20.m1.1.12.1"" xref=""S0.Ex20.m1.1.12.1.pmml""><csymbol cd=""latexml"" id=""S0.Ex20.m1.1.1"" xref=""S0.Ex20.m1.1.1.pmml"">for-all</csymbol><ci id=""S0.Ex20.m1.1.2"" xref=""S0.Ex20.m1.1.2.pmml"">n</ci></apply><list id=""S0.Ex20.m1.1.12.2.1"" xref=""S0.Ex20.m1.1.12.2.pmml""><ci id=""S0.Ex20.m1.1.4"" xref=""S0.Ex20.m1.1.4.pmml"">N</ci><apply id=""S0.Ex20.m1.1.12.2.2"" xref=""S0.Ex20.m1.1.12.2.2.pmml""><times id=""S0.Ex20.m1.1.12.2.2.1"" xref=""S0.Ex20.m1.1.12.2.2.1.pmml""/><ci id=""S0.Ex20.m1.1.6"" xref=""S0.Ex20.m1.1.6.pmml"">n</ci><ci id=""S0.Ex20.m1.1.7"" xref=""S0.Ex20.m1.1.7.pmml"">&amp;</ci><ci id=""S0.Ex20.m1.1.8"" xref=""S0.Ex20.m1.1.8.pmml"">g</ci><ci id=""S0.Ex20.m1.1.9"" xref=""S0.Ex20.m1.1.9.pmml"">t</ci></apply><cn id=""S0.Ex20.m1.1.11"" type=""integer"" xref=""S0.Ex20.m1.1.11.pmml"">3</cn></list></apply></math>"
q_1029	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""n=4"" class=""ltx_Math"" display=""block"" id=""S0.Ex21.m1.1""><apply id=""S0.Ex21.m1.1.4"" xref=""S0.Ex21.m1.1.4.pmml""><eq id=""S0.Ex21.m1.1.2"" xref=""S0.Ex21.m1.1.2.pmml""/><ci id=""S0.Ex21.m1.1.1"" xref=""S0.Ex21.m1.1.1.pmml"">n</ci><cn id=""S0.Ex21.m1.1.3"" type=""integer"" xref=""S0.Ex21.m1.1.3.pmml"">4</cn></apply></math>"
q_1030	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""k"" class=""ltx_Math"" display=""block"" id=""S0.Ex22.m1.1""><ci id=""S0.Ex22.m1.1.1"" xref=""S0.Ex22.m1.1.1.pmml"">k</ci></math>"
q_1031	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""n=k"" class=""ltx_Math"" display=""block"" id=""S0.Ex23.m1.1""><apply id=""S0.Ex23.m1.1.4"" xref=""S0.Ex23.m1.1.4.pmml""><eq id=""S0.Ex23.m1.1.2"" xref=""S0.Ex23.m1.1.2.pmml""/><ci id=""S0.Ex23.m1.1.1"" xref=""S0.Ex23.m1.1.1.pmml"">n</ci><ci id=""S0.Ex23.m1.1.3"" xref=""S0.Ex23.m1.1.3.pmml"">k</ci></apply></math>"
q_1032	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""k^{2}\leq 2^{k}"" class=""ltx_Math"" display=""block"" id=""S0.Ex24.m1.1""><apply id=""S0.Ex24.m1.1.6"" xref=""S0.Ex24.m1.1.6.pmml""><leq id=""S0.Ex24.m1.1.3"" xref=""S0.Ex24.m1.1.3.pmml""/><apply id=""S0.Ex24.m1.1.6.1"" xref=""S0.Ex24.m1.1.6.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex24.m1.1.6.1.1"" xref=""S0.Ex24.m1.1.6.1.pmml"">superscript</csymbol><ci id=""S0.Ex24.m1.1.1"" xref=""S0.Ex24.m1.1.1.pmml"">k</ci><cn id=""S0.Ex24.m1.1.2.1"" type=""integer"" xref=""S0.Ex24.m1.1.2.1.pmml"">2</cn></apply><apply id=""S0.Ex24.m1.1.6.2"" xref=""S0.Ex24.m1.1.6.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex24.m1.1.6.2.1"" xref=""S0.Ex24.m1.1.6.2.pmml"">superscript</csymbol><cn id=""S0.Ex24.m1.1.4"" type=""integer"" xref=""S0.Ex24.m1.1.4.pmml"">2</cn><ci id=""S0.Ex24.m1.1.5.1"" xref=""S0.Ex24.m1.1.5.1.pmml"">k</ci></apply></apply></math>"
q_1033	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""(k+1)^{2}\leq 2^{k+1}"" class=""ltx_Math"" display=""block"" id=""S0.Ex25.m1.1""><apply id=""S0.Ex25.m1.1.10"" xref=""S0.Ex25.m1.1.10.pmml""><leq id=""S0.Ex25.m1.1.7"" xref=""S0.Ex25.m1.1.7.pmml""/><apply id=""S0.Ex25.m1.1.10.1"" xref=""S0.Ex25.m1.1.10.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex25.m1.1.10.1.1"" xref=""S0.Ex25.m1.1.10.1.pmml"">superscript</csymbol><apply id=""S0.Ex25.m1.1.10.1.2.2"" xref=""S0.Ex25.m1.1.10.1.2.pmml""><plus id=""S0.Ex25.m1.1.3"" xref=""S0.Ex25.m1.1.3.pmml""/><ci id=""S0.Ex25.m1.1.2"" xref=""S0.Ex25.m1.1.2.pmml"">k</ci><cn id=""S0.Ex25.m1.1.4"" type=""integer"" xref=""S0.Ex25.m1.1.4.pmml"">1</cn></apply><cn id=""S0.Ex25.m1.1.6.1"" type=""integer"" xref=""S0.Ex25.m1.1.6.1.pmml"">2</cn></apply><apply id=""S0.Ex25.m1.1.10.2"" xref=""S0.Ex25.m1.1.10.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex25.m1.1.10.2.1"" xref=""S0.Ex25.m1.1.10.2.pmml"">superscript</csymbol><cn id=""S0.Ex25.m1.1.8"" type=""integer"" xref=""S0.Ex25.m1.1.8.pmml"">2</cn><apply id=""S0.Ex25.m1.1.9.1"" xref=""S0.Ex25.m1.1.9.1.pmml""><plus id=""S0.Ex25.m1.1.9.1.2"" xref=""S0.Ex25.m1.1.9.1.2.pmml""/><ci id=""S0.Ex25.m1.1.9.1.1"" xref=""S0.Ex25.m1.1.9.1.1.pmml"">k</ci><cn id=""S0.Ex25.m1.1.9.1.3"" type=""integer"" xref=""S0.Ex25.m1.1.9.1.3.pmml"">1</cn></apply></apply></apply></math>"
q_1034	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""=k^{2}\leq 2^{k}"" class=""ltx_Math"" display=""block"" id=""S0.Ex26.m1.1""><apply id=""S0.Ex26.m1.1.7"" xref=""S0.Ex26.m1.1.7.pmml""><and id=""S0.Ex26.m1.1.7a"" xref=""S0.Ex26.m1.1.7.pmml""/><apply id=""S0.Ex26.m1.1.7b"" xref=""S0.Ex26.m1.1.7.pmml""><eq id=""S0.Ex26.m1.1.1"" xref=""S0.Ex26.m1.1.1.pmml""/><csymbol cd=""latexml"" id=""S0.Ex26.m1.1.7.2"" xref=""S0.Ex26.m1.1.7.2.pmml"">absent</csymbol><apply id=""S0.Ex26.m1.1.7.3"" xref=""S0.Ex26.m1.1.7.3.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex26.m1.1.7.3.1"" xref=""S0.Ex26.m1.1.7.3.pmml"">superscript</csymbol><ci id=""S0.Ex26.m1.1.2"" xref=""S0.Ex26.m1.1.2.pmml"">k</ci><cn id=""S0.Ex26.m1.1.3.1"" type=""integer"" xref=""S0.Ex26.m1.1.3.1.pmml"">2</cn></apply></apply><apply id=""S0.Ex26.m1.1.7c"" xref=""S0.Ex26.m1.1.7.pmml""><leq id=""S0.Ex26.m1.1.4"" xref=""S0.Ex26.m1.1.4.pmml""/><apply id=""S0.Ex26.m1.1.7.3"" xref=""S0.Ex26.m1.1.7.3.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex26.m1.1.7.3.1"" xref=""S0.Ex26.m1.1.7.3.pmml"">superscript</csymbol><ci id=""S0.Ex26.m1.1.2"" xref=""S0.Ex26.m1.1.2.pmml"">k</ci><cn id=""S0.Ex26.m1.1.3.1"" type=""integer"" xref=""S0.Ex26.m1.1.3.1.pmml"">2</cn></apply><apply id=""S0.Ex26.m1.1.7.4"" xref=""S0.Ex26.m1.1.7.4.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex26.m1.1.7.4.1"" xref=""S0.Ex26.m1.1.7.4.pmml"">superscript</csymbol><cn id=""S0.Ex26.m1.1.5"" type=""integer"" xref=""S0.Ex26.m1.1.5.pmml"">2</cn><ci id=""S0.Ex26.m1.1.6.1"" xref=""S0.Ex26.m1.1.6.1.pmml"">k</ci></apply></apply></apply></math>"
q_1035	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""=2k^{2}\leq 2^{k+1}"" class=""ltx_Math"" display=""block"" id=""S0.Ex27.m1.1""><apply id=""S0.Ex27.m1.1.8"" xref=""S0.Ex27.m1.1.8.pmml""><and id=""S0.Ex27.m1.1.8a"" xref=""S0.Ex27.m1.1.8.pmml""/><apply id=""S0.Ex27.m1.1.8b"" xref=""S0.Ex27.m1.1.8.pmml""><eq id=""S0.Ex27.m1.1.1"" xref=""S0.Ex27.m1.1.1.pmml""/><csymbol cd=""latexml"" id=""S0.Ex27.m1.1.8.2"" xref=""S0.Ex27.m1.1.8.2.pmml"">absent</csymbol><apply id=""S0.Ex27.m1.1.8.3"" xref=""S0.Ex27.m1.1.8.3.pmml""><times id=""S0.Ex27.m1.1.8.3.1"" xref=""S0.Ex27.m1.1.8.3.1.pmml""/><cn id=""S0.Ex27.m1.1.2"" type=""integer"" xref=""S0.Ex27.m1.1.2.pmml"">2</cn><apply id=""S0.Ex27.m1.1.8.3.2"" xref=""S0.Ex27.m1.1.8.3.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex27.m1.1.8.3.2.1"" xref=""S0.Ex27.m1.1.8.3.2.pmml"">superscript</csymbol><ci id=""S0.Ex27.m1.1.3"" xref=""S0.Ex27.m1.1.3.pmml"">k</ci><cn id=""S0.Ex27.m1.1.4.1"" type=""integer"" xref=""S0.Ex27.m1.1.4.1.pmml"">2</cn></apply></apply></apply><apply id=""S0.Ex27.m1.1.8c"" xref=""S0.Ex27.m1.1.8.pmml""><leq id=""S0.Ex27.m1.1.5"" xref=""S0.Ex27.m1.1.5.pmml""/><apply id=""S0.Ex27.m1.1.8.3"" xref=""S0.Ex27.m1.1.8.3.pmml""><times id=""S0.Ex27.m1.1.8.3.1"" xref=""S0.Ex27.m1.1.8.3.1.pmml""/><cn id=""S0.Ex27.m1.1.2"" type=""integer"" xref=""S0.Ex27.m1.1.2.pmml"">2</cn><apply id=""S0.Ex27.m1.1.8.3.2"" xref=""S0.Ex27.m1.1.8.3.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex27.m1.1.8.3.2.1"" xref=""S0.Ex27.m1.1.8.3.2.pmml"">superscript</csymbol><ci id=""S0.Ex27.m1.1.3"" xref=""S0.Ex27.m1.1.3.pmml"">k</ci><cn id=""S0.Ex27.m1.1.4.1"" type=""integer"" xref=""S0.Ex27.m1.1.4.1.pmml"">2</cn></apply></apply><apply id=""S0.Ex27.m1.1.8.4"" xref=""S0.Ex27.m1.1.8.4.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex27.m1.1.8.4.1"" xref=""S0.Ex27.m1.1.8.4.pmml"">superscript</csymbol><cn id=""S0.Ex27.m1.1.6"" type=""integer"" xref=""S0.Ex27.m1.1.6.pmml"">2</cn><apply id=""S0.Ex27.m1.1.7.1"" xref=""S0.Ex27.m1.1.7.1.pmml""><plus id=""S0.Ex27.m1.1.7.1.2"" xref=""S0.Ex27.m1.1.7.1.2.pmml""/><ci id=""S0.Ex27.m1.1.7.1.1"" xref=""S0.Ex27.m1.1.7.1.1.pmml"">k</ci><cn id=""S0.Ex27.m1.1.7.1.3"" type=""integer"" xref=""S0.Ex27.m1.1.7.1.3.pmml"">1</cn></apply></apply></apply></apply></math>"
q_1036	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""(k+1)^{2}\leq 2k^{2}"" class=""ltx_Math"" display=""block"" id=""S0.Ex28.m1.1""><apply id=""S0.Ex28.m1.1.11"" xref=""S0.Ex28.m1.1.11.pmml""><leq id=""S0.Ex28.m1.1.7"" xref=""S0.Ex28.m1.1.7.pmml""/><apply id=""S0.Ex28.m1.1.11.1"" xref=""S0.Ex28.m1.1.11.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex28.m1.1.11.1.1"" xref=""S0.Ex28.m1.1.11.1.pmml"">superscript</csymbol><apply id=""S0.Ex28.m1.1.11.1.2.2"" xref=""S0.Ex28.m1.1.11.1.2.pmml""><plus id=""S0.Ex28.m1.1.3"" xref=""S0.Ex28.m1.1.3.pmml""/><ci id=""S0.Ex28.m1.1.2"" xref=""S0.Ex28.m1.1.2.pmml"">k</ci><cn id=""S0.Ex28.m1.1.4"" type=""integer"" xref=""S0.Ex28.m1.1.4.pmml"">1</cn></apply><cn id=""S0.Ex28.m1.1.6.1"" type=""integer"" xref=""S0.Ex28.m1.1.6.1.pmml"">2</cn></apply><apply id=""S0.Ex28.m1.1.11.2"" xref=""S0.Ex28.m1.1.11.2.pmml""><times id=""S0.Ex28.m1.1.11.2.1"" xref=""S0.Ex28.m1.1.11.2.1.pmml""/><cn id=""S0.Ex28.m1.1.8"" type=""integer"" xref=""S0.Ex28.m1.1.8.pmml"">2</cn><apply id=""S0.Ex28.m1.1.11.2.2"" xref=""S0.Ex28.m1.1.11.2.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex28.m1.1.11.2.2.1"" xref=""S0.Ex28.m1.1.11.2.2.pmml"">superscript</csymbol><ci id=""S0.Ex28.m1.1.9"" xref=""S0.Ex28.m1.1.9.pmml"">k</ci><cn id=""S0.Ex28.m1.1.10.1"" type=""integer"" xref=""S0.Ex28.m1.1.10.1.pmml"">2</cn></apply></apply></apply></math>"
q_1037	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""(k+1)^{2}\leq 2^{k+1}"" class=""ltx_Math"" display=""block"" id=""S0.Ex29.m1.1""><apply id=""S0.Ex29.m1.1.10"" xref=""S0.Ex29.m1.1.10.pmml""><leq id=""S0.Ex29.m1.1.7"" xref=""S0.Ex29.m1.1.7.pmml""/><apply id=""S0.Ex29.m1.1.10.1"" xref=""S0.Ex29.m1.1.10.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex29.m1.1.10.1.1"" xref=""S0.Ex29.m1.1.10.1.pmml"">superscript</csymbol><apply id=""S0.Ex29.m1.1.10.1.2.2"" xref=""S0.Ex29.m1.1.10.1.2.pmml""><plus id=""S0.Ex29.m1.1.3"" xref=""S0.Ex29.m1.1.3.pmml""/><ci id=""S0.Ex29.m1.1.2"" xref=""S0.Ex29.m1.1.2.pmml"">k</ci><cn id=""S0.Ex29.m1.1.4"" type=""integer"" xref=""S0.Ex29.m1.1.4.pmml"">1</cn></apply><cn id=""S0.Ex29.m1.1.6.1"" type=""integer"" xref=""S0.Ex29.m1.1.6.1.pmml"">2</cn></apply><apply id=""S0.Ex29.m1.1.10.2"" xref=""S0.Ex29.m1.1.10.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex29.m1.1.10.2.1"" xref=""S0.Ex29.m1.1.10.2.pmml"">superscript</csymbol><cn id=""S0.Ex29.m1.1.8"" type=""integer"" xref=""S0.Ex29.m1.1.8.pmml"">2</cn><apply id=""S0.Ex29.m1.1.9.1"" xref=""S0.Ex29.m1.1.9.1.pmml""><plus id=""S0.Ex29.m1.1.9.1.2"" xref=""S0.Ex29.m1.1.9.1.2.pmml""/><ci id=""S0.Ex29.m1.1.9.1.1"" xref=""S0.Ex29.m1.1.9.1.1.pmml"">k</ci><cn id=""S0.Ex29.m1.1.9.1.3"" type=""integer"" xref=""S0.Ex29.m1.1.9.1.3.pmml"">1</cn></apply></apply></apply></math>"
q_1038	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""(k+1)^{2}≤2k^{2}"" class=""ltx_Math"" display=""block"" id=""S0.Ex30.m1.1""><apply id=""S0.Ex30.m1.1.11"" xref=""S0.Ex30.m1.1.11.pmml""><times id=""S0.Ex30.m1.1.11.1"" xref=""S0.Ex30.m1.1.11.1.pmml""/><apply id=""S0.Ex30.m1.1.11.2"" xref=""S0.Ex30.m1.1.11.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex30.m1.1.11.2.1"" xref=""S0.Ex30.m1.1.11.2.pmml"">superscript</csymbol><apply id=""S0.Ex30.m1.1.11.2.2.2"" xref=""S0.Ex30.m1.1.11.2.2.pmml""><plus id=""S0.Ex30.m1.1.3"" xref=""S0.Ex30.m1.1.3.pmml""/><ci id=""S0.Ex30.m1.1.2"" xref=""S0.Ex30.m1.1.2.pmml"">k</ci><cn id=""S0.Ex30.m1.1.4"" type=""integer"" xref=""S0.Ex30.m1.1.4.pmml"">1</cn></apply><cn id=""S0.Ex30.m1.1.6.1"" type=""integer"" xref=""S0.Ex30.m1.1.6.1.pmml"">2</cn></apply><ci id=""S0.Ex30.m1.1.7"" xref=""S0.Ex30.m1.1.7.pmml"">≤</ci><cn id=""S0.Ex30.m1.1.8"" type=""integer"" xref=""S0.Ex30.m1.1.8.pmml"">2</cn><apply id=""S0.Ex30.m1.1.11.3"" xref=""S0.Ex30.m1.1.11.3.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex30.m1.1.11.3.1"" xref=""S0.Ex30.m1.1.11.3.pmml"">superscript</csymbol><ci id=""S0.Ex30.m1.1.9"" xref=""S0.Ex30.m1.1.9.pmml"">k</ci><cn id=""S0.Ex30.m1.1.10.1"" type=""integer"" xref=""S0.Ex30.m1.1.10.1.pmml"">2</cn></apply></apply></math>"
q_1039	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""=k^{2}+2k+1\leq 2k^{2}"" class=""ltx_Math"" display=""block"" id=""S0.Ex31.m1.1""><apply id=""S0.Ex31.m1.1.13"" xref=""S0.Ex31.m1.1.13.pmml""><and id=""S0.Ex31.m1.1.13a"" xref=""S0.Ex31.m1.1.13.pmml""/><apply id=""S0.Ex31.m1.1.13b"" xref=""S0.Ex31.m1.1.13.pmml""><eq id=""S0.Ex31.m1.1.1"" xref=""S0.Ex31.m1.1.1.pmml""/><csymbol cd=""latexml"" id=""S0.Ex31.m1.1.13.2"" xref=""S0.Ex31.m1.1.13.2.pmml"">absent</csymbol><apply id=""S0.Ex31.m1.1.13.3"" xref=""S0.Ex31.m1.1.13.3.pmml""><plus id=""S0.Ex31.m1.1.4"" xref=""S0.Ex31.m1.1.4.pmml""/><apply id=""S0.Ex31.m1.1.13.3.1"" xref=""S0.Ex31.m1.1.13.3.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex31.m1.1.13.3.1.1"" xref=""S0.Ex31.m1.1.13.3.1.pmml"">superscript</csymbol><ci id=""S0.Ex31.m1.1.2"" xref=""S0.Ex31.m1.1.2.pmml"">k</ci><cn id=""S0.Ex31.m1.1.3.1"" type=""integer"" xref=""S0.Ex31.m1.1.3.1.pmml"">2</cn></apply><apply id=""S0.Ex31.m1.1.13.3.2"" xref=""S0.Ex31.m1.1.13.3.2.pmml""><times id=""S0.Ex31.m1.1.13.3.2.1"" xref=""S0.Ex31.m1.1.13.3.2.1.pmml""/><cn id=""S0.Ex31.m1.1.5"" type=""integer"" xref=""S0.Ex31.m1.1.5.pmml"">2</cn><ci id=""S0.Ex31.m1.1.6"" xref=""S0.Ex31.m1.1.6.pmml"">k</ci></apply><cn id=""S0.Ex31.m1.1.8"" type=""integer"" xref=""S0.Ex31.m1.1.8.pmml"">1</cn></apply></apply><apply id=""S0.Ex31.m1.1.13c"" xref=""S0.Ex31.m1.1.13.pmml""><leq id=""S0.Ex31.m1.1.9"" xref=""S0.Ex31.m1.1.9.pmml""/><apply id=""S0.Ex31.m1.1.13.3"" xref=""S0.Ex31.m1.1.13.3.pmml""><plus id=""S0.Ex31.m1.1.4"" xref=""S0.Ex31.m1.1.4.pmml""/><apply id=""S0.Ex31.m1.1.13.3.1"" xref=""S0.Ex31.m1.1.13.3.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex31.m1.1.13.3.1.1"" xref=""S0.Ex31.m1.1.13.3.1.pmml"">superscript</csymbol><ci id=""S0.Ex31.m1.1.2"" xref=""S0.Ex31.m1.1.2.pmml"">k</ci><cn id=""S0.Ex31.m1.1.3.1"" type=""integer"" xref=""S0.Ex31.m1.1.3.1.pmml"">2</cn></apply><apply id=""S0.Ex31.m1.1.13.3.2"" xref=""S0.Ex31.m1.1.13.3.2.pmml""><times id=""S0.Ex31.m1.1.13.3.2.1"" xref=""S0.Ex31.m1.1.13.3.2.1.pmml""/><cn id=""S0.Ex31.m1.1.5"" type=""integer"" xref=""S0.Ex31.m1.1.5.pmml"">2</cn><ci id=""S0.Ex31.m1.1.6"" xref=""S0.Ex31.m1.1.6.pmml"">k</ci></apply><cn id=""S0.Ex31.m1.1.8"" type=""integer"" xref=""S0.Ex31.m1.1.8.pmml"">1</cn></apply><apply id=""S0.Ex31.m1.1.13.4"" xref=""S0.Ex31.m1.1.13.4.pmml""><times id=""S0.Ex31.m1.1.13.4.1"" xref=""S0.Ex31.m1.1.13.4.1.pmml""/><cn id=""S0.Ex31.m1.1.10"" type=""integer"" xref=""S0.Ex31.m1.1.10.pmml"">2</cn><apply id=""S0.Ex31.m1.1.13.4.2"" xref=""S0.Ex31.m1.1.13.4.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex31.m1.1.13.4.2.1"" xref=""S0.Ex31.m1.1.13.4.2.pmml"">superscript</csymbol><ci id=""S0.Ex31.m1.1.11"" xref=""S0.Ex31.m1.1.11.pmml"">k</ci><cn id=""S0.Ex31.m1.1.12.1"" type=""integer"" xref=""S0.Ex31.m1.1.12.1.pmml"">2</cn></apply></apply></apply></apply></math>"
q_1040	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""=2k+1\leq k^{2}"" class=""ltx_Math"" display=""block"" id=""S0.Ex32.m1.1""><apply id=""S0.Ex32.m1.1.9"" xref=""S0.Ex32.m1.1.9.pmml""><and id=""S0.Ex32.m1.1.9a"" xref=""S0.Ex32.m1.1.9.pmml""/><apply id=""S0.Ex32.m1.1.9b"" xref=""S0.Ex32.m1.1.9.pmml""><eq id=""S0.Ex32.m1.1.1"" xref=""S0.Ex32.m1.1.1.pmml""/><csymbol cd=""latexml"" id=""S0.Ex32.m1.1.9.2"" xref=""S0.Ex32.m1.1.9.2.pmml"">absent</csymbol><apply id=""S0.Ex32.m1.1.9.3"" xref=""S0.Ex32.m1.1.9.3.pmml""><plus id=""S0.Ex32.m1.1.4"" xref=""S0.Ex32.m1.1.4.pmml""/><apply id=""S0.Ex32.m1.1.9.3.1"" xref=""S0.Ex32.m1.1.9.3.1.pmml""><times id=""S0.Ex32.m1.1.9.3.1.1"" xref=""S0.Ex32.m1.1.9.3.1.1.pmml""/><cn id=""S0.Ex32.m1.1.2"" type=""integer"" xref=""S0.Ex32.m1.1.2.pmml"">2</cn><ci id=""S0.Ex32.m1.1.3"" xref=""S0.Ex32.m1.1.3.pmml"">k</ci></apply><cn id=""S0.Ex32.m1.1.5"" type=""integer"" xref=""S0.Ex32.m1.1.5.pmml"">1</cn></apply></apply><apply id=""S0.Ex32.m1.1.9c"" xref=""S0.Ex32.m1.1.9.pmml""><leq id=""S0.Ex32.m1.1.6"" xref=""S0.Ex32.m1.1.6.pmml""/><apply id=""S0.Ex32.m1.1.9.3"" xref=""S0.Ex32.m1.1.9.3.pmml""><plus id=""S0.Ex32.m1.1.4"" xref=""S0.Ex32.m1.1.4.pmml""/><apply id=""S0.Ex32.m1.1.9.3.1"" xref=""S0.Ex32.m1.1.9.3.1.pmml""><times id=""S0.Ex32.m1.1.9.3.1.1"" xref=""S0.Ex32.m1.1.9.3.1.1.pmml""/><cn id=""S0.Ex32.m1.1.2"" type=""integer"" xref=""S0.Ex32.m1.1.2.pmml"">2</cn><ci id=""S0.Ex32.m1.1.3"" xref=""S0.Ex32.m1.1.3.pmml"">k</ci></apply><cn id=""S0.Ex32.m1.1.5"" type=""integer"" xref=""S0.Ex32.m1.1.5.pmml"">1</cn></apply><apply id=""S0.Ex32.m1.1.9.4"" xref=""S0.Ex32.m1.1.9.4.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex32.m1.1.9.4.1"" xref=""S0.Ex32.m1.1.9.4.pmml"">superscript</csymbol><ci id=""S0.Ex32.m1.1.7"" xref=""S0.Ex32.m1.1.7.pmml"">k</ci><cn id=""S0.Ex32.m1.1.8.1"" type=""integer"" xref=""S0.Ex32.m1.1.8.1.pmml"">2</cn></apply></apply></apply></math>"
q_1041	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""=2k+1\leq 2^{k}"" class=""ltx_Math"" display=""block"" id=""S0.Ex33.m1.1""><apply id=""S0.Ex33.m1.1.9"" xref=""S0.Ex33.m1.1.9.pmml""><and id=""S0.Ex33.m1.1.9a"" xref=""S0.Ex33.m1.1.9.pmml""/><apply id=""S0.Ex33.m1.1.9b"" xref=""S0.Ex33.m1.1.9.pmml""><eq id=""S0.Ex33.m1.1.1"" xref=""S0.Ex33.m1.1.1.pmml""/><csymbol cd=""latexml"" id=""S0.Ex33.m1.1.9.2"" xref=""S0.Ex33.m1.1.9.2.pmml"">absent</csymbol><apply id=""S0.Ex33.m1.1.9.3"" xref=""S0.Ex33.m1.1.9.3.pmml""><plus id=""S0.Ex33.m1.1.4"" xref=""S0.Ex33.m1.1.4.pmml""/><apply id=""S0.Ex33.m1.1.9.3.1"" xref=""S0.Ex33.m1.1.9.3.1.pmml""><times id=""S0.Ex33.m1.1.9.3.1.1"" xref=""S0.Ex33.m1.1.9.3.1.1.pmml""/><cn id=""S0.Ex33.m1.1.2"" type=""integer"" xref=""S0.Ex33.m1.1.2.pmml"">2</cn><ci id=""S0.Ex33.m1.1.3"" xref=""S0.Ex33.m1.1.3.pmml"">k</ci></apply><cn id=""S0.Ex33.m1.1.5"" type=""integer"" xref=""S0.Ex33.m1.1.5.pmml"">1</cn></apply></apply><apply id=""S0.Ex33.m1.1.9c"" xref=""S0.Ex33.m1.1.9.pmml""><leq id=""S0.Ex33.m1.1.6"" xref=""S0.Ex33.m1.1.6.pmml""/><apply id=""S0.Ex33.m1.1.9.3"" xref=""S0.Ex33.m1.1.9.3.pmml""><plus id=""S0.Ex33.m1.1.4"" xref=""S0.Ex33.m1.1.4.pmml""/><apply id=""S0.Ex33.m1.1.9.3.1"" xref=""S0.Ex33.m1.1.9.3.1.pmml""><times id=""S0.Ex33.m1.1.9.3.1.1"" xref=""S0.Ex33.m1.1.9.3.1.1.pmml""/><cn id=""S0.Ex33.m1.1.2"" type=""integer"" xref=""S0.Ex33.m1.1.2.pmml"">2</cn><ci id=""S0.Ex33.m1.1.3"" xref=""S0.Ex33.m1.1.3.pmml"">k</ci></apply><cn id=""S0.Ex33.m1.1.5"" type=""integer"" xref=""S0.Ex33.m1.1.5.pmml"">1</cn></apply><apply id=""S0.Ex33.m1.1.9.4"" xref=""S0.Ex33.m1.1.9.4.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex33.m1.1.9.4.1"" xref=""S0.Ex33.m1.1.9.4.pmml"">superscript</csymbol><cn id=""S0.Ex33.m1.1.7"" type=""integer"" xref=""S0.Ex33.m1.1.7.pmml"">2</cn><ci id=""S0.Ex33.m1.1.8.1"" xref=""S0.Ex33.m1.1.8.1.pmml"">k</ci></apply></apply></apply></math>"
q_1042	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""(k+1)^{2}\leq 2k^{2}"" class=""ltx_Math"" display=""block"" id=""S0.Ex34.m1.1""><apply id=""S0.Ex34.m1.1.11"" xref=""S0.Ex34.m1.1.11.pmml""><leq id=""S0.Ex34.m1.1.7"" xref=""S0.Ex34.m1.1.7.pmml""/><apply id=""S0.Ex34.m1.1.11.1"" xref=""S0.Ex34.m1.1.11.1.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex34.m1.1.11.1.1"" xref=""S0.Ex34.m1.1.11.1.pmml"">superscript</csymbol><apply id=""S0.Ex34.m1.1.11.1.2.2"" xref=""S0.Ex34.m1.1.11.1.2.pmml""><plus id=""S0.Ex34.m1.1.3"" xref=""S0.Ex34.m1.1.3.pmml""/><ci id=""S0.Ex34.m1.1.2"" xref=""S0.Ex34.m1.1.2.pmml"">k</ci><cn id=""S0.Ex34.m1.1.4"" type=""integer"" xref=""S0.Ex34.m1.1.4.pmml"">1</cn></apply><cn id=""S0.Ex34.m1.1.6.1"" type=""integer"" xref=""S0.Ex34.m1.1.6.1.pmml"">2</cn></apply><apply id=""S0.Ex34.m1.1.11.2"" xref=""S0.Ex34.m1.1.11.2.pmml""><times id=""S0.Ex34.m1.1.11.2.1"" xref=""S0.Ex34.m1.1.11.2.1.pmml""/><cn id=""S0.Ex34.m1.1.8"" type=""integer"" xref=""S0.Ex34.m1.1.8.pmml"">2</cn><apply id=""S0.Ex34.m1.1.11.2.2"" xref=""S0.Ex34.m1.1.11.2.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex34.m1.1.11.2.2.1"" xref=""S0.Ex34.m1.1.11.2.2.pmml"">superscript</csymbol><ci id=""S0.Ex34.m1.1.9"" xref=""S0.Ex34.m1.1.9.pmml"">k</ci><cn id=""S0.Ex34.m1.1.10.1"" type=""integer"" xref=""S0.Ex34.m1.1.10.1.pmml"">2</cn></apply></apply></apply></math>"
q_1043	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""n=4"" class=""ltx_Math"" display=""block"" id=""S0.Ex35.m1.1""><apply id=""S0.Ex35.m1.1.4"" xref=""S0.Ex35.m1.1.4.pmml""><eq id=""S0.Ex35.m1.1.2"" xref=""S0.Ex35.m1.1.2.pmml""/><ci id=""S0.Ex35.m1.1.1"" xref=""S0.Ex35.m1.1.1.pmml"">n</ci><cn id=""S0.Ex35.m1.1.3"" type=""integer"" xref=""S0.Ex35.m1.1.3.pmml"">4</cn></apply></math>"
q_1044	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""j,k=j"" class=""ltx_Math"" display=""block"" id=""S0.Ex36.m1.1""><apply id=""S0.Ex36.m1.1.6"" xref=""S0.Ex36.m1.1.6.pmml""><eq id=""S0.Ex36.m1.1.4"" xref=""S0.Ex36.m1.1.4.pmml""/><list id=""S0.Ex36.m1.1.6.1.1"" xref=""S0.Ex36.m1.1.6.1.pmml""><ci id=""S0.Ex36.m1.1.1"" xref=""S0.Ex36.m1.1.1.pmml"">j</ci><ci id=""S0.Ex36.m1.1.3"" xref=""S0.Ex36.m1.1.3.pmml"">k</ci></list><ci id=""S0.Ex36.m1.1.5"" xref=""S0.Ex36.m1.1.5.pmml"">j</ci></apply></math>"
q_1045	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML"" alttext=""2k+1\leq 2^{k}"" class=""ltx_Math"" display=""block"" id=""S0.Ex37.m1.1""><apply id=""S0.Ex37.m1.1.8"" xref=""S0.Ex37.m1.1.8.pmml""><leq id=""S0.Ex37.m1.1.5"" xref=""S0.Ex37.m1.1.5.pmml""/><apply id=""S0.Ex37.m1.1.8.1"" xref=""S0.Ex37.m1.1.8.1.pmml""><plus id=""S0.Ex37.m1.1.3"" xref=""S0.Ex37.m1.1.3.pmml""/><apply id=""S0.Ex37.m1.1.8.1.1"" xref=""S0.Ex37.m1.1.8.1.1.pmml""><times id=""S0.Ex37.m1.1.8.1.1.1"" xref=""S0.Ex37.m1.1.8.1.1.1.pmml""/><cn id=""S0.Ex37.m1.1.1"" type=""integer"" xref=""S0.Ex37.m1.1.1.pmml"">2</cn><ci id=""S0.Ex37.m1.1.2"" xref=""S0.Ex37.m1.1.2.pmml"">k</ci></apply><cn id=""S0.Ex37.m1.1.4"" type=""integer"" xref=""S0.Ex37.m1.1.4.pmml"">1</cn></apply><apply id=""S0.Ex37.m1.1.8.2"" xref=""S0.Ex37.m1.1.8.2.pmml""><csymbol cd=""ambiguous"" id=""S0.Ex37.m1.1.8.2.1"" xref=""S0.Ex37.m1.1.8.2.pmml"">superscript</csymbol><cn id=""S0.Ex37.m1.1.6"" type=""integer"" xref=""S0.Ex37.m1.1.6.pmml"">2</cn><ci id=""S0.Ex37.m1.1.7.1"" xref=""S0.Ex37.m1.1.7.1.pmml"">k</ci></apply></apply></math>"