Question

Find the sum of the following infinite geometric series, if it exists. 1/3+1/9+1/27+1/81+...

Answer 1

The given infinite geometric series is

`(1)/(3),\, (1)/(9), \, (1)/(27) , \, (1)/(81) , \, ...,`

The first term is a = 1/3.
The common ratio is r = 1/3.

The sum is

`(a)/(1-r)= (1/3)/(1 - 1/3) = (1)/(2)`

Answer: 1/2