Simplify : $$1 + {1 \over {1 + {2 \over {2 + {3 \over {1 + {4 \over 5}}}}}}}$$

A. $$1\frac{{11}}{{17}}$$

B. $$1\frac{{5}}{{7}}$$

C. $$1\frac{{6}}{{17}}$$

D. $$1\frac{{21}}{{17}}$$

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & 1 + \frac{1}{{1 + \frac{2}{{2 + \frac{3}{{1 + \frac{4}{5}}}}}}} \cr & = 1 + \frac{1}{{1 + \frac{2}{{2 + \frac{3}{{\frac{9}{5}}}}}}} \cr & = 1 + \frac{1}{{1 + \frac{2}{{2 + \frac{5}{3}}}}} \cr & = 1 + \frac{1}{{1 + \frac{2}{{\frac{{11}}{3}}}}} \cr & = 1 + \frac{1}{{1 + \frac{6}{{11}}}} \cr & = 1 + \frac{1}{{\frac{{17}}{{11}}}} \cr & = 1 + \frac{{11}}{{17}} \cr & = 1\frac{{11}}{{17}} \cr} $$