$latex \mathbf{\frac{100}{111}}&s=1$
Given Expression,
$latex = \frac{2}{2+\frac{2\times 0.39}{3+\frac{2}{3+\frac{2}{3}}}}&s=2$
$latex = \frac{2}{2+\frac{2\times 0.39}{3+\frac{2}{\frac{11}{3}}}}&s=2$
$latex = \frac{2}{2+\frac{2\times 0.39}{3+\frac{6}{11}}}&s=2$
$latex = \frac{2}{2+\frac{2\times 0.39}{\frac{33+6}{11}}}&s=2$
$latex = \frac{2}{2+\frac{11\times 2\times 0.39}{39}}&s=2$
$latex = \frac{2}{2+\frac{11\times 2}{39}\times \frac{39}{100}}&s=2$
$latex = \frac{2}{2+\frac{11}{50}} = \frac{2}{\frac{100+11}{50}}&s=2$
$latex = \frac{100}{111}&s=1$
Hence option [C] is right answer.