# How do you find the sum of the infinite geometric series 1 - 1/5 + 1/25 - 1/125 + ...?

Dec 26, 2015

$s = \frac{5}{6}$

#### Explanation:

We know that
$s = 1 - \frac{1}{5} + \frac{1}{25} - \frac{1}{125} + \ldots$
Multiplying 5 both the side we get
⇒5s=5-1+1/5-1/25+1/125 ...
⇒5s=5-1*(1-1/5+1/25-1/125 ...)
⇒5s=5-1*s
⇒5s=5-s
⇒6s=5
⇒s=5/6