# How do you find the sum of the infinite geometric series 2+2/3+2/9+2/27+...?

Jul 10, 2016

$3.$

#### Explanation:

Let $s$ denote the reqd. sum. Then, we know that,

$s = \frac{a}{1 - r}$, where, $a =$ the first term of the series, and, $r ,$common ratio, with $| r | < 1$.

Here, $a = 2$, and $r =$second term/first term$= \frac{\frac{2}{3}}{2} = \frac{1}{3}$, hence $| r | < 1.$

Therefore, $s = \frac{2}{1 - \frac{1}{3}} = \frac{2}{\frac{2}{3}} = 3$