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Question Number 142437 by mohammad17 last updated on 31/May/21

Answered by Dwaipayan Shikari last updated on 31/May/21

$$\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{n}\underset{n=1}{\sum ^{\mathrm{\infty }}}\sqrt{\frac{n}{n+r}}$$$$={\int }_0^1\frac{1}{\sqrt{1+x}}dx1+x=u^2$$$$=2{\int }_1^{\sqrt{2}}\frac{u}{u}du=2(\sqrt{2}-1)$$

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