# How do you find the sum of the infinite geometric series 1-(1/3) + (1/9) - (1/27) + .....?

Feb 22, 2016

The formula for sum of an infinite geometric series is ${s}_{\infty} = \frac{a}{1 - r}$

#### Explanation:

We must first find the common ratio, r, which can be found by using the formula $r = {t}_{2} / {t}_{1}$

$r = \frac{- \frac{1}{3}}{1}$

$r = - \frac{1}{3}$

a is the first term, 1.

${s}_{\infty} = \frac{1}{1 - \left(- \frac{1}{3}\right)}$

${s}_{\infty} = \frac{1}{\frac{4}{3}}$

${s}_{\infty} = \frac{3}{4}$

The sum is $\frac{3}{4}$.

Hopefully this helps!