A Pre-RMO question! -31

Algebra Level 2

Let Sn=k=0n1k+1+k\displaystyle S_n=\sum_{k=0}^{n}\frac{1}{\sqrt{k+1}+\sqrt{k}}. Find the value of n=1991Sn+Sn1\displaystyle \sum_{n=1}^{99} \frac{1}{S_n + S_{n-1}}.

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