JEE Mains · Maths · STD 12 - 7.2 definite integral
\(\lim _{n \rightarrow \infty}\left(\frac{1}{1+n}+\frac{1}{2+n}+\frac{1}{3+n}+\ldots+\frac{1}{2 n}\right)\) is equal to :-
- A \(0\)
- B \(\log _{ e } 2\)
- C \(\log _{ e }\left(\frac{3}{2}\right)\)
- D \(\log _{ e }\left(\frac{2}{3}\right)\)
Answer & Solution
Correct Answer
(B) \(\log _{ e } 2\)
Step-by-step Solution
Detailed explanation
\(\lim _{n \rightarrow \infty}\left(\frac{1}{1+n}+\ldots .+\frac{1}{n+n}\right)=\lim _{n \rightarrow \infty} \sum \limits_{r=1}^n \frac{1}{n+r}\) \(=\lim _{ n \rightarrow \infty} \sum \limits_{ r =1}^{ n } \frac{1}{ n }\left(\frac{1}{1+\frac{ r }{ n }}\right)\)…
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