1. Series formula

Any help with this question would be very much appreciated

2. Re: Series formula

Rationalize the denominator, and you will find you have a telescoping series.

3. Re: Series formula

Multiply nominator and denominator by the conjugate expression ( same expression with - sign in the middle) of the denominator....
the rest is easy as Mark Fl said in his post

4. Re: Series formula

I have rationalized the denominator but I don't actually know where to go from there, that is why I am posting this, I don't know the process

5. Re: Series formula

What did you get when you rationalized the denominator?

If you show your work, then we can better see where you are and how best to help.

6. Re: Series formula

sqrt(r+1)-sqrt(r)

7. Re: Series formula

Correct, so we now have:

$\displaystyle \sum_{r=1}^n\left(\sqrt{r+1}-\sqrt{r} \right)=\sum_{r=1}^n\sqrt{r+1}-\sum_{r=1}^n\sqrt{r}$

Now, can you change the index of summation on one of the sums so that you have the same summand in each?