Attachment 28433

Any help with this question would be very much appreciated :)

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- May 22nd 2013, 07:53 PMcalmo11Series formula
Attachment 28433

Any help with this question would be very much appreciated :) - May 22nd 2013, 08:00 PMMarkFLRe: Series formula
Rationalize the denominator, and you will find you have a telescoping series.

- May 22nd 2013, 10:31 PMMINOANMANRe: 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 PMcalmo11Re: 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 PMMarkFLRe: 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 PMcalmo11Re: Series formula
sqrt(r+1)-sqrt(r)

- May 23rd 2013, 07:18 PMMarkFLRe: 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?