The value of lim n → ∞ 1 n ∑ j = 1 n 2 j - 1 + 8 n 2 j - 1 + 4 n is equal to:

1. $5+{\log }_e\left(\frac{3}{2}\right)$
2. $2-{\log }_e\left(\frac{2}{3}\right)$
3. $3+2{\log }_e\left(\frac{2}{3}\right)$
4. $1+2{\log }_e\left(\frac{3}{2}\right)$

Solution

Asked in: JEE Main 2021 (27 Jul Shift 1)

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