AP EAMCET · Maths · Definite Integration
\(\lim _{n \rightarrow \infty}\left(\frac{1}{\sqrt{n^2}}+\frac{1}{\sqrt{n^2-1}}+\ldots .+\frac{1}{\sqrt{n^2-(n-1)^2}}\right)=\)
- A \(2 \sqrt{\pi}\)
- B \(\frac{2}{\sqrt{\pi}}\)
- C \(\frac{\pi}{2}\)
- D \(\frac{3 \pi}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{\rightarrow \infty}\left(\frac{1}{\sqrt{n^2}}+\frac{1}{\sqrt{n^2-1}}+\ldots+\frac{1}{\sqrt{n^2-(n-1)^2}}\right) \\ & =\lim _{n \rightarrow \infty} \frac{1}{n}\left(1+\frac{1}{\sqrt{1-\frac{1}{n^2}}}+\ldots+\frac{1}{\sqrt{1-\frac{(n-1)^2}{n^2}}}\right) \\…
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