Summation problem __

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November 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 ?

Thanks in advance
Nikolas
November 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 ?

Thanks in advance
Nikolas

$\sum_{n=0}^{\infty}x^{2n} <br />$
November 3rd 2010, 09:50 AM
tsebamm

Quote:

Originally Posted by Also sprach Zarathustra

$\sum_{n=0}^{\infty}x^{2n} <br />$

thanks for your quick reply. Can you explain a bit your answer?
November 3rd 2010, 09:58 AM
Also sprach Zarathustra

Geometric series - Wikipedia, the free encyclopedia
November 3rd 2010, 02:10 PM
TheCoffeeMachine

You know that $\frac{1}{1-t} = \sum_{n=0}^{\infty}t^n$ . If $t = x^2$ , then $\frac{1}{1-x^2} = \sum_{n=0}^{\infty}(x^2)^n = \sum_{n=0}^{\infty}{x}^{2n}$ .
November 3rd 2010, 04:23 PM
tsebamm

Quote:

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!

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