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$\underset{n \to \infty}{L t} [\frac{\sqrt{n + 1} + \sqrt{n + 2} + .... + \sqrt{n + n}}{n \sqrt{n}}]$

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222−13

22−13

22+13

None of these

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detailed solution

Correct option is A

limn→∞1+1n+1+2n+…..+1+nnlimn→∞∑r=1n 1+rn=∫01 1+xdx=23(1+x)3/201=2323/2−1=2(22−1)3

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Ltn→∞n+1+n+2+....+n+nnn

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$\underset{n \to \infty}{L t} [\frac{\sqrt{n + 1} + \sqrt{n + 2} + .... + \sqrt{n + n}}{n \sqrt{n}}]$