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
`(a)/(1-r)`.

Here the given series is
`(1)/(7) +(1)/(49) +(1)/(343) +...`.

Here
`a=1,r=(1)/(7)`. The sum of the infinite geometric series is

`(1)/(1-1/7) =(7)/(6)`