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Math Help - Prove equality sums

  1. #1
    Senior Member DeMath's Avatar
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    Prove equality of sums

    Prove

    \sum \limits_{n=1}^{m}\frac{1}{n(n+k)}=\frac{m}{k}\sum \limits_{n=1}^{k}\frac{1}{n(n+m)}
    Last edited by DeMath; September 13th 2012 at 10:20 AM.
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    Re: Prove equality sums

    Quote Originally Posted by DeMath View Post
    Prove

    \sum \limits_{n=1}^{m}\frac{1}{n(n+k)}=\frac{m}{k}\sum \limits_{n=1}^{k}\frac{1}{n(n+m)}
    Can you write either of them as a telescoping series using Partial Fractions?
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    Senior Member DeMath's Avatar
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    Re: Prove equality sums

    Quote Originally Posted by Prove It View Post
    Can you write either of them as a telescoping series using Partial Fractions?
    Of course I can, but after what will you do with these fractions?
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    Re: Prove equality sums

    Quote Originally Posted by DeMath View Post
    Of course I can, but after what will you do with these fractions?
    Do you know what is meant by a telescoping series?
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  5. #5
    Senior Member DeMath's Avatar
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    Re: Prove equality sums

    Quote Originally Posted by Prove It View Post
    Do you know what is meant by a telescoping series?
    I know it and how to prove my equality.

    If I understand correctly, in this section of the forum members offer interesting problems to solve, but do not ask how to solve.


    P.S. Sorry for my English.
    Last edited by DeMath; September 13th 2012 at 07:43 AM.
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    Re: Prove equality sums

    Quote Originally Posted by DeMath View Post
    I know it and how to prove my equality.

    If I understand correctly, in this section of the forum members offer interesting problems to solve, but do not ask how to solve.


    P.S. Sorry for my English.
    Oh I see, haha. I should have read which subforum this question was in.
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