Ta có: $\frac{1}{3^3}<\frac{1}{2.3.4}=$$\frac{1}{2}($ $\frac{1}{2.3}$ -$\frac{1}{3.4}$ )
Tương tự: $\frac{1}{4^3}<\frac{1}{3.4.5}=$$\frac{1}{2}($ $\frac{1}{3.4}$ -$\frac{1}{4.5}$ )
.....
$\frac{1}{11^3}<\frac{1}{10.11.12}=$$\frac{1}{2}($ $\frac{1}{10.11}$ -$\frac{1}{11.12}$ )
Suy ra: VT=$\frac{1}{2}$($\frac{1}{2.3}$-$\frac{1}{11.12}$)=$\frac{1}{12}$- $\frac{1}{2.11.12}$ < $\frac{1}{12}$ =VP
⇒Đpcm