Question

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

Answer 1

`s=5/6`

Explanation:

We know that
`s=1-1/5+1/25-1/125+ ...`
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`