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Math Help - summation identity proof

  1. #1
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    summation identity proof

    I have been trying to find a proof for the following summation identity.


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

    I have found that we can prove this using the differentiation, but was wondering if there is another way to prove that, i.e., without using the differentiation
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by led5v View Post
    I have been trying to find a proof for the following summation identity.


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

    I have found that we can prove this using the differentiation, but was wondering if there is another way to prove that, i.e., without using the differentiation
    Binomial expansion of (1-x)^(-2) followed by a bit of simplification should do it.

    RonL
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