# What is the sum of this infinite geometric series 2 + 1 + 1/2 + 1/4 + 1/8...?

Sum $= 4$

#### Explanation:

The common ratio with the range $- 1$<$r$<$1$

the formula is $S = {a}_{1} / \left(1 - r\right)$

We will use this formula because, $r = \frac{1}{2}$

Sum $S = {a}_{1} / \left(1 - r\right) = \frac{2}{1 - \frac{1}{2}} = 4$

God bless....I hope the explanation is useful...