# How do you find the sum of the infinite geometric series 2-2+2-2+..?

##### 1 Answer

The series diverges by typical summation methods, but may converge depending on the method used.

#### Explanation:

In general, a geometric series will diverge if the common ratio

Still, let's look at this case in a little more detail.

A series

Typically, we refer to *partial sum* of the series (often denoted

For the series in question, we have

As the sequence

(the fact that the sequence

The particular series mentioned is similar to a famous series known as Grandi's Series. Like Grandi's series, it diverges in conventional summation, but may converge if another method, such as Cesàro summation, is used.

Numberphile has a nice video on the subject here