find-sum-1-1-2-1-2-3-1-2019-2020-

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}} + \dots + \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} + \dots + \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}} \dots w h i c h a r e \sqrt{4} - \sqrt{3}, \sqrt{5} - \sqrt{4} \dots . .