## A blog for enthusiastic math-lovers!

### Telescoping problem

The following problem is also a telescoping problem which is found on the 2005 Purple Comet Competition, #20. Please comment if you have any ideas! Note that it uses similar techniques as some of the previous problems that I posted, so please work on them also!

The summation $\sum_{k=1}^{360} \frac{1}{k\sqrt{k+1}+(k+1)\sqrt{k}}$ is the ratio of two relatively prime positive integers $m$ and $n$. Find $m+n$.