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Let Sn=∑k=0n1k+1+k\displaystyle S_n=\sum_{k=0}^{n}\frac{1}{\sqrt{k+1}+\sqrt{k}}Sn=k=0∑nk+1+k1. Find the value of ∑n=1991Sn+Sn−1\displaystyle \sum_{n=1}^{99} \frac{1}{S_n + S_{n-1}}n=1∑99Sn+Sn−11.
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