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Math Help - Power Series

  1. #1
    Junior Member
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    Power Series

    Find a power series representation for the function and determine the raidus of convergence.

    f(x) = x^2/(1-2x)^2

    Im having trouble isolating it to 1/1-x.

    Anyone who can hint me something would be greatly appreciated. You do not need to solve it, please help me simplify it to 1/1-x. Thanks.
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  2. #2
    Senior Member
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    Re: Power Series

    Try using the fact that \dfrac{d}{dx}\left ( \dfrac{1}{1-x}\right ) = \dfrac{1}{(1-x)^2} to obtain the series for \dfrac{1}{(1-x)^2} from \dfrac{1}{1-x} = 1 + x + x^2 + \cdots and proceed from there.

    --Kevin C.
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  3. #3
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    f(x) = x^2/(1-2x)^2

    what I do with the 2x?
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  4. #4
    Senior Member
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    Re: Power Series

    If you have a series for \dfrac{1}{(1-u)^2}, then just subtitute u=2x to get a series for \dfrac{1}{(1-2x)^2} and proceed from there.

    --Kevin C.
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