# How do you find the sum of 1/7^2+1/7^3+...+1/7^(n+1)+...?

Feb 19, 2017

$\frac{1}{42}$

#### Explanation:

This is of the form of the geometric series

$a + a r + a {r}^{2} + \ldots + a {r}^{n} \to \frac{a}{1 - r}$, as n to oo#.

a = 1/7^2 and r = 1/7, and so, the limit is

$\frac{1}{7} ^ \frac{2}{1 - \frac{1}{7}} = \frac{1}{42}$..