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Step by step video, text & image solution for The value of (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+....+(1)/(sqrt(8)+sqrt(9))

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manvithmarupudi
The value of the series

\[
\frac{1}{1+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{3}} + \frac{1}{\sqrt{3}+\sqrt{4}} + \cdots + \frac{1}{\sqrt{8}+\sqrt{9}}
\]

is \(\boxed{2}\).

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