find sum (1/(1 + (√2))) + (1/( (√2) + (√3))) + ... + (1/( (√(2019)) + (√(2020))))


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Question Number 123661 by weltr last updated on 27/Nov/20

$f i n d s u m \frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + . . . + \frac{1}{\sqrt{2019} + \sqrt{2020}}$
	Answered by Dwaipayan Shikari last updated on 27/Nov/20

	$\frac{1}{1 + \sqrt{2}} = \sqrt{2} - 1$ $\frac{1}{\sqrt{2} + \sqrt{3}} = \sqrt{3} - \sqrt{2}$ $s u m = \sqrt{2} - 1 + \sqrt{3} - \sqrt{2} + \sqrt{4} - \sqrt{3} + . . . + \sqrt{2020} - \sqrt{2019}$ $= \sqrt{2020} - 1$
	Commented by weltr last updated on 27/Nov/20

	$t h a n k s, b u t w h e r e d i d y o u g e t \sqrt{4} - \sqrt{3} f r o m ?$
	Commented by Dwaipayan Shikari last updated on 27/Nov/20

	$O t h e r t e r m s a r e \frac{1}{\sqrt{4} + \sqrt{3}}, \frac{1}{\sqrt{4} + \sqrt{5}} . . . w h i c h a r e \sqrt{4} - \sqrt{3}, \sqrt{5} - \sqrt{4} . . . . .$
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