Cho dãy số

- Hướng dẫn giải

Đáp án là B

Ta có: $lim u_n=lim\left(n-1\right)\sqrt{\frac{2n+2}{n^4+n^2-1}}$

$=lim\sqrt{\frac{{\left(n-1\right)}^2\left(2n+2\right)}{n^4+n^2-1}}$
$=lim\sqrt{\frac{2n^3-2n^2-2n+2}{n^4+n^2-1}}$

$$\begin{gathered} =lim\sqrt{\frac{{\displaystyle \frac{2}{n}}-{\displaystyle \frac{2}{n^2}}-{\displaystyle \frac{2}{n^3}}+{\displaystyle \frac{2}{n^4}}}{1+{\displaystyle \frac{1}{n^2}}-{\displaystyle \frac{1}{n^4}}}}=0 \\ Vi lim (\frac{2}{n}-\frac{2}{n^2}-\frac{2}{n^3}+\frac{2}{n^4}) = 0- 0- 0+\hspace{0.17em}0 = 0 \\ lim (1+\frac{1}{n^2}-\frac{1}{n^4}) = 1 +\hspace{0.17em}0- 0 = 1 \end{gathered}$$