Aptitude Question ID : 94797

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

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

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