5
Given that
$latex x= 1 +\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}}&s=1$
$latex = 1+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{3}{2}}}} = 1+\frac{1}{1+\frac{1}{1+\frac{2}{3}}}&s=1$
$latex = 1+\frac{1}{1+\frac{1}{\frac{5}{3}}} = 1+\frac{1}{1+\frac{3}{5}}&s=1$
$latex = 1+\frac{1}{\frac{8}{5}} = 1+\frac{5}{8} = \frac{13}{8}&s=1$
$latex \therefore 2x + \frac{7}{4} = 2\times \frac{13}{8}+\frac{7}{4}&s=1$
$latex = \frac{13+7}{4} = \frac{20}{4} = 5&s=1$
Hence option [C] is right answer.