Use the properties of geometric series to find the sum of the series. For what values of the variable does the series converge to this sum?

Question

Use the properties of geometric series to find the sum of the series. For what values of the variable does the series converge to this sum?
5−10z+20z^(2)−40z^(3)+?
sum =

domain =
(Give your domain as an interval or comma separated list of intervals; for example, to enter the region x<−1 and 2<x≤3, enter (-infinity,-1), (2,3].)

Answer 1

Each term is obtained by multiplying the preceding term by -2z. It will converge if l-2zl <1, so                               domain for z is (-1/2,1/2).

 

The sum would be S = -5/(1 + 2z), because the general formula for the sum of an infinite geometric series = a/(1 - r)