# How do you find the sum of the infinite geometric series given a_1=4 and r=5/7?

Feb 3, 2017

See explanation.

#### Explanation:

A geometric series is convergent if and only if its ratio $r$ is between -1 and 1.

Here the ratio is $r = \frac{5}{7}$, so the series is covergent.

The sum can be calculated as:

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

so here we have:

$S = \frac{4}{1 - \frac{5}{7}} = \frac{4}{\frac{2}{7}} = 4 \cdot \frac{7}{2} = 14$