# Prove equality sums

• Sep 13th 2012, 05:51 AM
DeMath
Prove equality of sums
Prove

$\sum \limits_{n=1}^{m}\frac{1}{n(n+k)}=\frac{m}{k}\sum \limits_{n=1}^{k}\frac{1}{n(n+m)}$
• Sep 13th 2012, 06:00 AM
Prove It
Re: Prove equality sums
Quote:

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?
• Sep 13th 2012, 06:37 AM
DeMath
Re: Prove equality sums
Quote:

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?
• Sep 13th 2012, 07:05 AM
Prove It
Re: Prove equality sums
Quote:

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?
• Sep 13th 2012, 07:39 AM
DeMath
Re: Prove equality sums
Quote:

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.
• Sep 13th 2012, 09:50 AM
Prove It
Re: Prove equality sums
Quote:

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.