# How do you find the sum of the convergent series 0.9-0.09+0.009-...? If the convergent series is not convergent, how do you know?

##### 1 Answer

Dec 30, 2015

#### Answer:

Note that the common ratio has an absolute value less than one, and use the geometric series formula to find that

#### Explanation:

A geometric series is a series of the form

where

If

An explanation of where this sum comes from is given in this answer.

For the given series, we have

Thus

As