# Summation problem __

• Nov 3rd 2010, 09:21 AM
tsebamm
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 ?

Nikolas
• Nov 3rd 2010, 09:27 AM
Also sprach Zarathustra
Quote:

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 ?

Nikolas

$\displaystyle \sum_{n=0}^{\infty}x^{2n}$
• Nov 3rd 2010, 09:50 AM
tsebamm
Quote:

Originally Posted by Also sprach Zarathustra
$\displaystyle \sum_{n=0}^{\infty}x^{2n}$

• Nov 3rd 2010, 09:58 AM
Also sprach Zarathustra
• Nov 3rd 2010, 02:10 PM
TheCoffeeMachine
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 PM
tsebamm
Quote:

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

I proved it about an hour ago. Thanks anyway!
Cheers!