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
$\frac{1}{3},\, \frac{1}{9}, \, \frac{1}{27} , \, \frac{1}{81} , \, ...,$

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

The sum is
$\frac{a}{1-r}= \frac{1/3}{1 - 1/3} = \frac{1}{2}$

Answer:  1/2