# Sum of Geometric Series

1. Sum the Geometric Series 1-x+x2-x3+x4

and hence simplify the function

[f(x)]4 = 1 - x5
1-x+x2-x3+x4

## Homework Equations

3. Not sure I quite get understand this properly, as my attempt doesnt seem quite right.

Basically Ive gotten

S=1-x+x2-x3+x4

S=1-1+x-x2+x3
x x

which then subtracted becomes

s(1 - 1) = (1-1)+2x+x+x
x x

= 1 +4x
x

Then, putting that into the simplifying function part gives me

f(x) =

1 -x5
-1 +4x
x

Last edited:

## Answers and Replies

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Notice that

$$1-x+x^2-x^3+\ldots=\sum_{n=0}^{\infty}(-1)^nx^n=\sum_{n=0}^{\infty}(-x)^n$$