Bài giải:
10.Ta nhân liên hợp với $\sqrt{n+1}+\sqrt{n-1}$,ta có:
$U_{n}$=$\frac{(\sqrt{n+1}-\sqrt{n-1}).(\sqrt{n+1}+\sqrt{n-1})}{\sqrt{n+1}+\sqrt{n-1}}$
=$\frac{n+1-(n-1)}{\sqrt{n+1}+\sqrt{n-1}}$
=$\frac{2}{\sqrt{n+1}+\sqrt{n-1}}$
=>$limU_{n}=lim(\frac{2}{\sqrt{n+1}+\sqrt{n-1}})=0$ (A)
2.Đề 2
$lim\frac{sin(n+1)}{n^2-5n}$
Ta có:
$\frac{sin(n+1)}{n^2-5n}$ $\leq \frac{1}{n^2-5n}$
Mà $lim\frac{1}{n^2-5n}=0$
=>$lim\frac{sin(n+1)}{n^2-5n}=0$
