Prove equality sums

**DeMath** · September 13th 2012, 05:51 AM

Prove

$\sum \limits_{n=1}^{m}\frac{1}{n(n+k)}=\frac{m}{k}\sum \limits_{n=1}^{k}\frac{1}{n(n+m)}$

**Prove It** · September 13th 2012, 06:00 AM

Originally Posted by DeMath

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?

**DeMath** · September 13th 2012, 06:37 AM

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?

**Prove It** · September 13th 2012, 07:05 AM

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?

**DeMath** · September 13th 2012, 07:39 AM

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.

**Prove It** · September 13th 2012, 09:50 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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