Knowing that 1/(1-x) = Σ x^n , for n=0 to inf.

Can anyone help me to find a power series summation rule for the function 1/(1-x^2) .

And also for which values does it converge ?

Thanks in advance

Nikolas

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- Nov 3rd 2010, 09:21 AMtsebammSummation problem __
Knowing that 1/(1-x) = Σ x^n , for n=0 to inf.

Can anyone help me to find a power series summation rule for the function 1/(1-x^2) .

And also for which values does it converge ?

Thanks in advance

Nikolas - Nov 3rd 2010, 09:27 AMAlso sprach Zarathustra
- Nov 3rd 2010, 09:50 AMtsebamm
- Nov 3rd 2010, 09:58 AMAlso sprach Zarathustra
- Nov 3rd 2010, 02:10 PMTheCoffeeMachine
You know that $\displaystyle \frac{1}{1-t} = \sum_{n=0}^{\infty}t^n$. If $\displaystyle t = x^2$, then $\displaystyle \frac{1}{1-x^2} = \sum_{n=0}^{\infty}(x^2)^n = \sum_{n=0}^{\infty}{x}^{2n}$.

- Nov 3rd 2010, 04:23 PMtsebamm