AP EAMCET · Maths · Definite Integration
If \(k \in N\) then \(\lim _{n \rightarrow \infty}\left[\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\ldots+\frac{1}{k n}\right]=\)
- A \(\log (k+1)\)
- B \(\log \mathrm{k}\)
- C \(\log (k+5)\)
- D \(\log (\mathrm{k}+1)-\log 6\)
Answer & Solution
Correct Answer
(B) \(\log \mathrm{k}\)
Step-by-step Solution
Detailed explanation
\( \lim _{n \rightarrow \infty}\left[\frac{1}{n+1}+\frac{1}{n+2}+\ldots+\frac{1}{k n}\right] = \lim _{n \rightarrow \infty} \sum_{r=n+1}^{k n} \frac{1}{r} \) \( = \lim _{n \rightarrow \infty} \sum_{r=n+1}^{k n} \frac{1}{n} \left(\frac{1}{r/n}\right) \)…
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