Question

How do you find the sum of the convergent series 0.1+0.01+0.001+...? If the convergent series is not convergent, how do you know?

Answer 1

`x=1/9`

Explanation:

Take

`x=0.1+0.01+.001+0.0001....`

But

`0.1+x/10=0.1+0.01+.001+0.0001....`

Therefore:

`x=0.1+x/10`

`10x=1+x`

`9x=1`

`x=1/9`