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Math Help - Power series representation

  1. #1
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    Power series representation

    Hi I assume this question is quite simple, but I am just not able to crack it.
    So I have to find the interval and radius of convergence for the function f(x). I am completely stumped as to how I can transform this into power series representation. All I can think of so far is saying that f(x) = d/dx(some nasty artan function). Is it possible to represent the function, as partial fractions?

    f(x) = 5/(2+8(x-1)^2)

    All help greatly appreciated.
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  2. #2
    MHF Contributor chisigma's Avatar
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    For |x-1|<\frac{1}{2} is...

    \displaystyle f(x)= \frac{5}{2+8\ (x-1)^{2}} = \frac{5}{2}\ \frac{1}{1+4\ (x-1)^{2}} = \frac{5}{2} \ \{1-4\ (x-1)^{2} + 16\ (x-1)^{4} - 64\ (x-1)^{6} +...\}

    Kind regards

    \chi \sigma
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