A) \[2\sqrt{2}\]
B) \[2\sqrt{2}-1\]
C) 2
D) 4
Correct Answer: C
Solution :
\[\underset{n\to \infty }{\mathop{Lim}}\,\,\,\frac{1}{n}\left[ 1+\sqrt{\frac{n}{n+1}}+\sqrt{\frac{n}{n+2}}+\sqrt{\frac{n}{n+3}}+.....+\sqrt{\frac{n}{4n}} \right]\]\[=\underset{n\to \infty }{\mathop{Lim}}\,\,\,\frac{1}{n}\left( \sum\limits_{r=0}^{3n}{\frac{1}{\sqrt{1+r/n}}} \right)=\int_{0}^{3}{\frac{1}{\sqrt{1+x}}}\,\,dx=2.\]
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