# How do you find the sum of the infinite geometric series 7 + 28/5 + 112/25 + 448/125?

Nov 11, 2015

Common ratio $= \frac{4}{5} < 1$
Since the ratio is less than 1 , the series converges and the sum exists.

#### Explanation:

Infinite Sum $= {a}_{1} / \left(1 - r\right)$

Infinite Sum $= \frac{7}{1 - \frac{4}{5}} = 35$

hope that helped