# ?How do you find the sum of the infinite geometric series 1 - x + x^2 - x^3 + x^4 ...?

Apr 15, 2018

See explanation.

#### Explanation:

A geometric series is convergent if and only if its common ratio is between $- 1$ and $1$, and its sum is then defined as:

## $S = {a}_{1} / \left(1 - q\right)$

So in the given task we have:

${a}_{1} = 1$ and $q = - x$.

According to the given condition we can say that:

If x in (-1;1) then the series has a finite sum and it is: