Evaluate:$$\text{ } 1 +\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots$$​

Correct option is A

Given:

​$$\text{ } 1 +\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots$$

Formula  Used:

Sum of terms in an infinite GP  = $$\frac{a}{(1-r)}$$​​

Solution:

$$\text{ } 1 +\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots$$

This is GP series 

a = 1 , r = $$\frac{1}{2}$$​​

Sum of the series  = $$\frac{a}{(1-r)}$$ 

= $$\frac{1}{(1-1/2)}$$

= 2