# power series and center of convergence

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• July 18th 2012, 02:32 PM
jsauce59
power series and center of convergence
I have a function g(x)=(2a)/(x^2-a^2) where a is some number greater than zero. I need to find a power series with a center of convergence at zero and then find the radius and the interval of convergence. Any help would be appreciated. Thanks
• July 18th 2012, 02:44 PM
girdav
Re: power series and center of convergence
Write it as $\frac{-2a}{a^2-x^2}=\frac{-2}a\frac 1{1-\left(\frac xa\right)^2}$ in order to use the expansion of $\frac 1{1+t^2}$ in power series.