# Math Help - Summation problem __

1. ## Summation 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

2. Originally Posted by tsebamm
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
$\sum_{n=0}^{\infty}x^{2n}
$

3. Originally Posted by Also sprach Zarathustra
$\sum_{n=0}^{\infty}x^{2n}
$
thanks for your quick reply. Can you explain a bit your answer?

4. You know that $\frac{1}{1-t} = \sum_{n=0}^{\infty}t^n$. If $t = x^2$, then $\frac{1}{1-x^2} = \sum_{n=0}^{\infty}(x^2)^n = \sum_{n=0}^{\infty}{x}^{2n}$.

5. Originally Posted by TheCoffeeMachine
You know that $\frac{1}{1-t} = \sum_{n=0}^{\infty}t^n$. If $t = x^2$, then $\frac{1}{1-x^2} = \sum_{n=0}^{\infty}(x^2)^n = \sum_{n=0}^{\infty}{x}^{2n}$.
I proved it about an hour ago. Thanks anyway!
Cheers!