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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: [JEE…

Q1

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:

[JEE Main 2021, 27 Jul (Shift 1)]

a

\(2-\log _e\left(\frac{2}{3}\right)\)

b

\(1+2 \log _e\left(\frac{3}{2}\right)\)

c

\(5+\log _e\left(\frac{3}{2}\right)\)

d

\(3+2 \log _e\left(\frac{2}{3}\right)\)

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