WBJEE · Maths · Definite Integration
\(\lim _{n \rightarrow \infty} \frac{\sqrt{1}+\sqrt{2}+\ldots+\sqrt{n-1}}{n \sqrt{n}}\) is equal to
- A \(\frac{1}{2}\)
- B \(\frac{1}{3}\)
- C \(\frac{2}{3}\)
- D 0
Answer & Solution
Correct Answer
(C) \(\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
\(\lim _{n \rightarrow \infty} \frac{\sqrt{1}+\sqrt{2}+\ldots+\sqrt{n-1}}{n \sqrt{n}}\) \(=\lim _{n \rightarrow \infty}\left(\frac{\sqrt{1}+\sqrt{2}+\ldots+\sqrt{n-1}+\sqrt{n}}{n \sqrt{n}}-\frac{n}{n \times n}\right)\)…
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