1/[ n*sqrt(n+1) + (n+1)*sqrt(n) ] finding sum of this serie

Hello,

I am trying to solve this series:

I have tried partial decomposition (telescoping series) process but it results very complicated and incorrect and then I get stack.

Have anyone an idea how the partial decompostion should be done so I get a result that the terms start to canceling them self. I don't want to bother anymore, just that part is enough and I will continue with the rest of the solution.

Thank you everyone!

Re: 1/[ n*sqrt(n+1) + (n+1)*sqrt(n) ] finding sum of this serie

You probably need to start by rationalising the denominator.

Now try the Partial Fractions decomposition.

Re: 1/[ n*sqrt(n+1) + (n+1)*sqrt(n) ] finding sum of this serie

Re: 1/[ n*sqrt(n+1) + (n+1)*sqrt(n) ] finding sum of this serie

Quote:

Originally Posted by

**Prove It** You probably need to start by rationalising the denominator.

Now try the Partial Fractions decomposition.

What's with the last step? From the second last step, I think you can separate it into two fractions:

EDIT: now I realised that the last step might have been a hint towards breaking it into two fractions, as in above!