1. ## Prove equality of sums

Prove

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

2. ## Re: Prove equality sums

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?

3. ## Re: Prove equality sums

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?

4. ## Re: Prove equality sums

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?

5. ## Re: Prove equality sums

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.

6. ## Re: Prove equality sums

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.