?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: