Question Number 128341 by liberty last updated on 06/Jan/21
$$\mathrm{Which}\:\mathrm{is}\:\mathrm{larger}\:\mathrm{Z}\:=\:\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{6}−\frac{\mathrm{4}}{\mathrm{11}}}}\:\mathrm{or}\:\mathrm{S}\:=\:\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{6}−\frac{\mathrm{5}}{\mathrm{11}}}}\:? \\ $$
Commented by mr W last updated on 06/Jan/21
$${without}\:{calculation}: \\ $$$${Z}:\:{larger}\nearrow{smaller}\nearrow{larger} \\ $$$$\Rightarrow{Z}\:{is}\:{larger}\:{than}\:{S}. \\ $$
Commented by MJS_new last updated on 06/Jan/21
$$\mathrm{I}'\mathrm{m}\:\mathrm{afraid}\:\mathrm{it}'\mathrm{s}\:\mathrm{the}\:\mathrm{other}\:\mathrm{way}\:\mathrm{round}... \\ $$
Commented by mr W last updated on 06/Jan/21
$${yes}\:{sir},\:{i}\:{misread}. \\ $$
Commented by MJS_new last updated on 06/Jan/21
$$\mathrm{I}\:\mathrm{thought}\:\mathrm{so} \\ $$
Commented by liberty last updated on 07/Jan/21
$$\mathrm{hahahaha}=== \\ $$
Answered by bramlexs22 last updated on 07/Jan/21
$$\mathrm{Z}=\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}}{\frac{\mathrm{62}}{\mathrm{11}}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{33}}{\mathrm{62}}}=\frac{\mathrm{62}}{\mathrm{157}}\approx\mathrm{0}.\mathrm{3949} \\ $$$$\mathrm{S}=\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}}{\frac{\mathrm{61}}{\mathrm{11}}}}=\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{33}}{\mathrm{61}}}\:=\:\frac{\mathrm{61}}{\mathrm{155}}\:\approx\mathrm{0}.\mathrm{3935} \\ $$$$\mathrm{then}\:\mathrm{Z}\:>\:\mathrm{S}\: \\ $$$$ \\ $$