# Series formula

• May 22nd 2013, 07:53 PM
calmo11
Series formula
Attachment 28433
Any help with this question would be very much appreciated :)
• May 22nd 2013, 08:00 PM
MarkFL
Re: Series formula
Rationalize the denominator, and you will find you have a telescoping series.
• May 22nd 2013, 10:31 PM
MINOANMAN
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
• May 23rd 2013, 06:24 PM
calmo11
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
• May 23rd 2013, 06:42 PM
MarkFL
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.
• May 23rd 2013, 06:53 PM
calmo11
Re: Series formula
sqrt(r+1)-sqrt(r)
• May 23rd 2013, 07:18 PM
MarkFL
Re: Series formula
Correct, so we now have:

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

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