Find the value of  $$4-\frac{5}{1+\frac{1}{3+\frac{1}{2 +\frac{1}{4}}}}$$​.

Correct option is A

Given: 

​$$4-\frac{5}{1+\frac{1}{3+\frac{1}{2 +\frac{1}{4}}}}$$     

Solution: 

​$$4-\frac{5}{1+\frac{1}{3+\frac{1}{2 +\frac{1}{4}}}} \\ \ \\ = 4-\frac{5}{1+\frac{1}{3+\frac{4}{9}}} \\ \ \\ = 4-\frac{5}{1+\frac{9}{31}} \\ \ \\ = 4-\frac{155}{40} \\ \ \\ = \frac{160-155}{40} \\ \ \\ = \frac{5}{40} \\ \ \\ = \frac{1}{8}$$​​