Ta có :
$\dfrac{1}{1.2}+\dfrac{1}{2.3}+....+\dfrac{1}{9.10}$
$=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}$
$=1-\dfrac{1}{10} < 1$
Ta có :
$\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+...+\dfrac{3}{17.20}$
$=\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{17}-\dfrac{1}{20}$
$=\dfrac{1}{2}-\dfrac{1}{20} < \dfrac{1}{2}$