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Math Help - power series sum-function!

  1. #1
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    power series sum-function!

    i have a power series of this form

     \sum_{n=1}^{\infty} \frac{(-1)^nx^n}{n}

    on attempting, i arrived at the sum-function

     \frac{x}{n(1+x)}

    pls help if i missed it.

    thanks
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  2. #2
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    Re: power series sum-function!

    The result MUST NOT contain n, because n is the variable index for sumation.
    Derive the sum in order to get a geometric sum.
    After expressing the geometric sum as a closed form, integrate it.
    Thanks from topsquark and lawochekel
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  3. #3
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    Re: power series sum-function!

    Your sum is the same as \sum_{n= 1}^\infty \frac{(-x)^n}{n}.

    Do you know the Taylor series for ln(x+ 1) about x= 0?
    Thanks from topsquark and lawochekel
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