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Archive for December, 2011

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 .


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