Evaluate: $$\frac1{2+\frac1{3+\frac1{4+\frac15}}}$$​

Correct option is B

Solution:

$$\frac{1}{2 + \frac{1}{3 + \frac{1}{4 + \frac{1}{5}}}} \\= \frac{1}{2 + \frac{1}{3 + \frac{1}{\frac{21}{5}}}}\\ = \frac{1}{2 + \frac{1}{\frac{68}{21}}} \\= \frac{1}{\frac{157}{68}} \\\ \\= \frac{68}{157}\\$$​