trước tiên ta biến đổi Ùn=$\frac{1}{\sqrt{n+1}+\sqrt{n}}$
$\rightarrow U_{n+1}=\frac{1}{\sqrt{n+2}+\sqrt{n+1}}$
xet hieu $U_{n+1}-U_{n}=\frac{1}{\sqrt{n+2}+\sqrt{n+1}}-\frac{1}{\sqrt{n+1}+\sqrt{n}}$
NX: $\sqrt{n+2}>\sqrt{n}\rightarrow \sqrt{n+2}+\sqrt{n+1}>\sqrt{n+1}+\sqrt{n}\rightarrow \frac{1}{\sqrt{n+2}+\sqrt{n+1}}<\frac{1}{\sqrt{n+1}+\sqrt{n}}$
hAY $U_{n+1}-U_{n}<0\rightarrow $ day giam