Question

Find the sum of this infinite geometric series 1/7+ 1/49 + 1/343

Answer 1

-1/6 or -1/8 or 1/6 or 1/8 one of these for sure 

Answer 2

The sum of the infinite geometric series

$a+ar+ar^2+...$ where $a$ is the first term and $r$ common ratio $-1<r<1$ is $\frac{a}{1-r}$.

Here the given series is $\frac{1}{7} +\frac{1}{49} +\frac{1}{343} +...$.

Here $a=1,r=\frac{1}{7}$. The sum of the infinite geometric series is

$\frac{1}{1-1/7} =\frac{7}{6}$