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 $\lim \,n\sqrt{{{u}_{n}}}.$
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