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Math Help - Help expressing a function as a power series

  1. #1
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    Help expressing a function as a power series

    Find the power series for (2+x)^(-3)

    I'm pretty sure I'm supposed to use a binomial series, but the formula for that is (1+x)^k. Since I have (2+x)^k, all I can think of is replacing x with u = x+1, and find (1+u)^(-3). Is this correct? I'm getting stuck in the middle of the problem using this method.
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    Hello,
    Quote Originally Posted by paulrb View Post
    Find the power series for (2+x)^(-3)

    I'm pretty sure I'm supposed to use a binomial series, but the formula for that is (1+x)^k. Since I have (2+x)^k, all I can think of is replacing x with u = x+1, and find (1+u)^(-3). Is this correct? I'm getting stuck in the middle of the problem using this method.
    More simply :

    2+x=\frac 12 (1+\tfrac x2)

    So (2+x)^{-3}=8 (1+\tfrac x2)^{-3}

    get it ?
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    Ok, that makes it much easier. Thanks.
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