Đặt \(f\left( n \right) = {\left( {{n^2} + n + 1}...

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