HMMT 2010 S5

Compute

$\sum_{n=1}^{98} \frac{2}{\sqrt{n}+\sqrt{n+2}}+\frac{1}{\sqrt{n+1}+\sqrt{n+2}}$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

3 \sqrt{11}-2 \sqrt{2}+19

Solutions

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