The value of the _ n [ 1 n^ 2 + 1 n^ 2 -1 + 1 n^ 2 -2^ 2 + + 1 n^ 2 -(n-1)^ 2 ] is
Mathematics · JEE Main · NTA Exams — Integral Calculus
The value of the
\[\lim _{n \rightarrow \infty}\left[\frac{1}{\sqrt{n^{2}}}+\frac{1}{\sqrt{n^{2}-1}}+\frac{1}{\sqrt{n^{2}-2^{2}}}+\ldots \ldots+\frac{1}{\sqrt{n^{2}-(n-1)^{2}}}\right]\]is
\[\lim _{n \rightarrow \infty}\left[\frac{1}{\sqrt{n^{2}}}+\frac{1}{\sqrt{n^{2}-1}}+\frac{1}{\sqrt{n^{2}-2^{2}}}+\ldots \ldots+\frac{1}{\sqrt{n^{2}-(n-1)^{2}}}\right]\]is
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{3}\)
- \(\frac{\pi}{2}\)
- none of these
Answer
(C) 2
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