The value of $$1 - \frac{1}{1 + \frac{1}{2 - \frac{1}{2 + \frac{1}{3}}}}$$​​ is:

Correct option is A

Given:
We are to evaluate the expression:

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

Solution:​

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

=$$1 - \frac{1}{1 + \frac{1}{2 - \frac{1}{\frac{7}{3}}}}$$

=$$1 - \frac{1}{1 + \frac{1}{2 - \frac{3}7}}$$

=$$1 - \frac{1}{1 + \frac{1}{ \frac{11}7}}$$​

=$$1 - \frac{1}{1 + \frac{7}{11}}$$

=$$1 - \frac{1}{ \frac{18}{11}}$$

=$$1-\frac{11}{18}$$ 

=$$\frac {18-11}{18}=\frac {7}{18}$$​​