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Welcome 2016! Part 38

Algebra Level 2

\[\large \dfrac{1}{1+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\cdots+\dfrac{1}{\sqrt{7}+\sqrt{8}}+\dfrac{1}{\sqrt{8}+\sqrt{9}} = \, ? \]

\[\sqrt{2}\] \[\infty\] 2 1 0

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by Anish Harsha

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