So sánh :3/1^2.2^2+5/2^2.3^2+7/3^2.4^2+...=19/9^2.10^2<1

$\frac{3}{1^2\cdot 2^2}+\frac{5}{2^2\cdot 3^2}+\frac{7}{3^2\cdot 4^2}+\dots +\frac{19}{9^2\cdot {10}^2}$ và 1

Ta có:

Vậy $\frac{3}{1^2\cdot 2^2}+\frac{5}{2^2\cdot 3^2}+\frac{7}{3^2\cdot 4^2}+\dots +\frac{19}{9^2\cdot {10}^2}<1$