# How do you find the sum of the infinite geometric series 5/4-1/4+1/20-1/100+...?

Feb 7, 2016

First, find the common ratio, r.

#### Explanation:

$r = {t}_{2} / {t}_{1}$

$r = \frac{- \frac{1}{4}}{\frac{5}{4}}$

$r = - \frac{1}{5}$

Now, we know all we need to know to find the sun, which can be found using the formula ${S}_{\infty} = \frac{a}{1 - r}$

${S}_{\infty} = \frac{\frac{5}{4}}{1 - \left(- \frac{1}{5}\right)}$

${S}_{\infty} = \frac{\frac{5}{4}}{\frac{6}{5}}$

${S}_{\infty} = \frac{25}{24}$

The sum of the series is $\frac{25}{24}$