S_{n}={\sum_{k=1}^{n}{\sqrt{k+2}-2\sqrt{k+1}+\sqrt{k}}}={\sum_{k=1}^{n}{\sqrt{k+2}}-2{\sum_{k=1}^{n}{\sqrt{k+1}}+{\sum_{k=1}^{n}{\sqrt{k}}}={\sum_{k=3}^{n+2}{\sqrt{k}}-2\sum_{k=2}^{n+1}{\sqrt{k}}+\sum_{k=1}^{n}{\sqrt{k}}}=