JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{j=1}^{n} \frac{(2 j-1)+8 n}{(2 j-1)+4 n}\) is equal to:
- A \(2-\log _{e}\left(\frac{2}{3}\right)\)
- B \(3+2 \log _{e}\left(\frac{2}{3}\right)\)
- C \(1+2 \log _{e}\left(\frac{3}{2}\right)\)
- D \(5+\log _{e}\left(\frac{3}{2}\right)\)
Answer & Solution
Correct Answer
(C) \(1+2 \log _{e}\left(\frac{3}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{j=1}^{n} \frac{\left(\frac{2 j}{n}-\frac{1}{n}+8\right)}{\left(\frac{2 j}{n}-\frac{1}{n}+4\right)}\) \(\int_{0}^{1} \frac{2 x+8}{2 x+4} d x=\int_{0}^{1} d x+\int_{0}^{1} \frac{4}{2 x+4} d x\)…
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