Đặt

Câu hỏi: Đặt $f\left(n\right)={\left(n^2+n+1\right)}^2+1$. Xét dãy số $\left(u_n\right)$ sao cho $u_n=\frac{f\left(1\right).f\left(3\right).f\left(5\right)\mathrm{...}f\left(2n-1\right)}{f\left(2\right).f\left(4\right).f\left(6\right)\mathrm{...}f\left(2n\right)}$. Tính $\lim n\sqrt{u_n}$

A. $\lim n\sqrt{u_n}=\sqrt{2}$ 

B. $\lim n\sqrt{u_n}=\frac{1}{\sqrt{3}}$

C. $\lim n\sqrt{u_n}=\sqrt{3}$

D. $\lim n\sqrt{u_n}=\frac{1}{\sqrt{2}}$