Question

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

Answer 1

`1/42`

Explanation:

This is of the form of the geometric series

`a + ar+ar^2+...+ar^n to a/(1-r)`, as n to oo#.

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

`1/7^2/(1-1/7)=1/42`..