$\displaystyle \sum_{n=1}^{\infty} x^n $

pls i don't have any ideal of finding thesum-functionof the above series, help.

thanks

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- May 28th 2013, 05:51 AMlawochekelpower series!
$\displaystyle \sum_{n=1}^{\infty} x^n $

pls i don't have any ideal of finding the**sum-function**of the above series, help.

thanks - May 28th 2013, 05:57 AMPlatoRe: power series!
- May 28th 2013, 06:24 PMProve ItRe: power series!
Under the conditions given by Plato, this would be an infinite geometric series. You should read more about geometric sequences and series.

- May 29th 2013, 01:54 AMKiwi_DaveRe: power series!
$\displaystyle \sum_{n=1}^{\infty} x^n=x + \sum_{n=2}^{\infty} x^n=x + x\sum_{n=1}^{\infty} x^n$

we have the original sum again on the right hand side (multiplied by x). So

$\displaystyle \sum_{n=1}^{\infty} x^n=x + x\sum_{n=1}^{\infty} x^n$

So

$\displaystyle (1-x)\sum_{n=1}^{\infty} x^n=x $

finally as others have said:

$\displaystyle \sum_{n=1}^{\infty} x^n=\frac{x}{1-x} $