# Math Help - geometric series

1. ## geometric series

find the sum for the infinite geometric series

3-3/2+3/4-...

1+1/3+1/9+...

2. Hi !

Originally Posted by gumi
find the sum for the infinite geometric series

3-3/2+3/4-...
$3-\frac 32+\frac 34+\dots=3 \left(1-\frac 12+\frac 1{2^2}-\dots\right)=3 \sum_{n=0}^\infty \left(-\frac 12\right)^n$

1+1/3+1/9+...
$=\sum_{n=0}^\infty \left(\frac 13\right)^n$

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If $|x|<1$, then $\sum_{n=0}^\infty x^n=\frac{1}{1-x}$

In general, we have :

$\sum_{n=0}^N x^n=\frac{1-x^{N+1}}{1-x}$