# How do you find the sum of the infinite geometric series 2/9+2/27+2/81+2/243+...?

Jan 10, 2016

Formula for infinite geometric sum ...

S_(oo)=a_1/(1-r

#### Explanation:

For this problem, $r = \frac{\frac{2}{27}}{\frac{2}{9}} = \frac{1}{3}$

${S}_{\infty} = \frac{\frac{2}{9}}{1 - \left(\frac{1}{3}\right)} = \frac{1}{3}$

hope that helped