The value of lim _n→∞ 1/n ∑^n _(j = 1) (2j - 1) + 8n/ (2j - 1) + 4n is equal to : (1) 5 + loge (3/2) (2) 2 - loge(2/3)

Question

The value of \(\lim\limits_{n \to \infty}\) \(\frac{1}{n}\) \(\displaystyle\sum_{j=1}^n\) \(\frac{(2j - 1) + 8n}{(2j - 1) + 4n} \) is equal to:

(1) 5 + log_e \(\left(\frac{3}{2}\right)\)

(2) 2 - log_e \(\left(\frac{2}{3}\right)\)

(3) 3 + 2log_e\(\left(\frac{2}{3}\right)\)

(4) 1 + 2log_e \(\left(\frac{3}{2}\right)\)

Answer 1

Correct option (4)

= 1 + 2ℓn \(\left(\frac{3}{2}\right)\)