$\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}+\dfrac{3}{14.17}+\dfrac{3}{17.20}$
$⇒ =\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+.....+\dfrac{1}{17}-\dfrac{1}{20}$
$⇒ =\dfrac{1}{2}-\dfrac{1}{20}$
$⇒ =\dfrac{1}{2}+\left(-\dfrac{1}{20}\right)$
$⇒ =\dfrac{10}{20}+\left(-\dfrac{1}{20}\right)$
$⇒ =\dfrac{9}{20}$
Chứng minh: $\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}+\dfrac{3}{14.17}+\dfrac{3}{17.20}=\dfrac{9}{20}<\dfrac{1}{2}$
Ta có: $\dfrac{1}{2}=\dfrac{1.10}{2.10}=\dfrac{10}{20}$
Vì $\dfrac{9}{20}<\dfrac{10}{20}⇒\dfrac{9}{20}<\dfrac{1}{2}$
Vậy $\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}+\dfrac{3}{14.17}+\dfrac{3}{17.20}<\dfrac{1}{2}$
