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  4. The value of (1/√10-√9)-(1/√11-√10)+(1/√12-√11) -....-(1/√121-√120) is equal to

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Q. The value of $ \frac{1}{\sqrt{10}-\sqrt{9}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{12}-\sqrt{11}} $ $ -....-\frac{1}{\sqrt{121}-\sqrt{120}} $ is equal to

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Solution:

We have $ \frac{1}{\sqrt{10}-\sqrt{9}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{12}-\sqrt{11}} $ $ -....-\frac{1}{\sqrt{121}-\sqrt{120}} $
$=\sqrt{10}+\sqrt{9}-\sqrt{11}-\sqrt{10}+\sqrt{12}+\sqrt{11} $ $ -.....-\sqrt{121}-\sqrt{120} $
$=\sqrt{9}-\sqrt{121}=3-11=-8 $