Prove $\displaystyle \sum \limits_{n=1}^{m}\frac{1}{n(n+k)}=\frac{m}{k}\sum \limits_{n=1}^{k}\frac{1}{n(n+m)}$
Last edited by DeMath; Sep 13th 2012 at 10:20 AM.
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Originally Posted by DeMath Prove $\displaystyle \sum \limits_{n=1}^{m}\frac{1}{n(n+k)}=\frac{m}{k}\sum \limits_{n=1}^{k}\frac{1}{n(n+m)}$ Can you write either of them as a telescoping series using Partial Fractions?
Originally Posted by Prove It 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?
Originally Posted by DeMath Of course I can, but after what will you do with these fractions? Do you know what is meant by a telescoping series?
Originally Posted by Prove It 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; Sep 13th 2012 at 07:43 AM.
Originally Posted by DeMath 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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