If S_ n = [ 1 2 n + 1 4 n^ 2 -1 + 1 4 n^ 2 -4 + + 1 3 n^ 2 +2 n-1 ] then _ n S_ n is…
Mathematics · JEE Main · NTA Exams — Integral Calculus
If \(S_{n}=\left[\frac{1}{2 n}+\frac{1}{\sqrt{4 n^{2}-1}}+\frac{1}{\sqrt{4 n^{2}-4}}+\ldots+\frac{1}{\sqrt{3 n^{2}+2 n-1}}\right]\)
then \(\lim _{n \rightarrow \infty} S_{n}\) is equal to
then \(\lim _{n \rightarrow \infty} S_{n}\) is equal to
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{6}\)
- \(\frac{\pi}{3}\)
- \(\frac{\pi}{2}\)
Answer
(B) 6
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