Aptitude Question ID : 94797

Find out the value of
$latex 1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{2}{3}}}}}&s=2$
[A]$latex \frac{8}{5}&s=1$
[B]$latex \frac{21}{13}&s=1$
[C]$latex \frac{34}{21}&s=1$
[D]$latex \frac{17}{3}&s=1$

$latex \mathbf{\frac{34}{21}}&s=1$
Given Expression,
$latex = 1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{2}{3}}}}}&s=2$
$latex = 1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{3+2}{3}}}}}= 1+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{5+3}{5}}}}&s=2$
$latex = 1+\frac{1}{1+\frac{1}{1+\frac{5}{8}}} = 1+\frac{1}{1+\frac{1}{\frac{8+5}{8}}}&s=2$
$latex = 1+\frac{1}{1+\frac{8}{13}} = 1+\frac{1}{\frac{13+8}{13}}&s=1$
$latex = 1+\frac{13}{21} = \frac{21+13}{21} = \frac{34}{21}&s=1$
Hence option [C] is right answer.


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