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Here is a hint to help you. $\displaystyle \frac{1}{{\sqrt k + \sqrt {k + 1} }} = \left( {\frac{1}{{\sqrt k + \sqrt {k + 1} }}} \right)\frac{{\sqrt k - \sqrt {k + 1} }}{{\sqrt k - \sqrt {k + 1} }} = \sqrt {k + 1} - \sqrt k $
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