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Math Help - Power series help

  1. #1
    Junior Member
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    Power series help

    f(x)=\frac{1}{4+x^2}
    a)write the first four terms and general term for the power series expansion of f about x=0
    b)find the radius of convergence of the series found in part a)


    Sorry but i don't really know how to do power series problems... I know
    \sum_{0}^{\infty}C_{n}X^n=C_{0}+C_{1}X+C_{2}X^2... but i don't really know what this means. Any Help?
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  2. #2
    MHF Contributor chisigma's Avatar
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    Is...

    f(x)= \frac{1}{4}\cdot \frac{1}{1+(\frac{x}{2})^{2}} (1)

    ... so that we can expand f(*) as 'geometric series' ...

    f(x) = \frac{1}{4}\cdot \sum_{n=0}^{\infty} (-1)^{n}\cdot (\frac{x}{2})^{2n} (2)

    ... that converges for |x|<2...

    Kind regards

    \chi \sigma
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