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

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Answer 1 · 2018-04-15T22:05:59

See 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:

$S=a_1/(1-q)$

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: