Simplify : 1 + 1 1 + 2 2 + 3 1 + 4 5

Answer: Option A

$$\begin{array}{rl}& 1+\frac{1}{1+\frac{2}{2+\frac{3}{1+\frac{4}{5}}}}\\ & =1+\frac{1}{1+\frac{2}{2+\frac{3}{\frac{9}{5}}}}\\ & =1+\frac{1}{1+\frac{2}{2+\frac{5}{3}}}\\ & =1+\frac{1}{1+\frac{2}{\frac{11}{3}}}\\ & =1+\frac{1}{1+\frac{6}{11}}\\ & =1+\frac{1}{\frac{17}{11}}\\ & =1+\frac{11}{17}\\ & =1\frac{11}{17}\end{array}$$