Đáp án: $x=17$
Giải thích các bước giải:
Ta có:
$\dfrac{1}{5}+\dfrac{1}{20}+\dfrac{1}{44}+...+\dfrac{2}{x(x+3)}=\dfrac{3}{10}$
$\to\dfrac{2}{10}+\dfrac{2}{40}+\dfrac{2}{88}+...+\dfrac{2}{x(x+3)}=\dfrac{3}{10}$
$\to\dfrac{1}{10}+\dfrac{1}{40}+\dfrac{1}{88}+...+\dfrac{1}{x(x+3)}=\dfrac{3}{20}$
$\to\dfrac{1}{2.5}+\dfrac{1}{5.8}+\dfrac{1}{8.11}+...+\dfrac{1}{x(x+3)}=\dfrac{3}{20}$
$\to\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+...+\dfrac{3}{x(x+3)}=\dfrac{9}{20}$
$\to\dfrac{5-2}{2.5}+\dfrac{8-5}{5.8}+\dfrac{11-8}{8.11}+...+\dfrac{x+3-x}{x(x+3)}=\dfrac{9}{20}$
$\to \dfrac12-\dfrac15+\dfrac15-\dfrac18+\dfrac18-\dfrac1{11}+...+\dfrac1x-\dfrac1{x+3}=\dfrac9{20}$
$\to\dfrac12-\dfrac1{x+3}=\dfrac9{20}$
$\to\dfrac1{x+3}=\dfrac12-\dfrac9{20}$
$\to \dfrac1{x+3}=\dfrac1{20}$
$\to x+3=20$
$\to x=17$
