Đáp án:
$x=\dfrac{11}{18}$
Giải thích các bước giải:
$\dfrac13+\dfrac16+\dfrac{1}{10}+\dfrac{1}{15}\ +\,.\!.\!.+\ \dfrac{1}{x.(2x+1)}=\dfrac{1}{10}\\\Rightarrow\dfrac16+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\ +\,.\!.\!.+\ \dfrac1{2x.(2x+1)}=\dfrac{1}{20}\\\Rightarrow \dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}\ +\,.\!.\!.+\ \dfrac{1}{2x.(2x+1)}=\dfrac{1}{20}\\\Rightarrow \dfrac12-\dfrac13+\dfrac13-\dfrac14+\dfrac14-\dfrac15+\dfrac15-\dfrac16\ +\,.\!.\!.+\ \dfrac{1}{2x}-\dfrac{1}{2x+1}=\dfrac{1}{20}\\\Rightarrow \dfrac12-\dfrac1{2x+1}=\dfrac1{20}\\\Rightarrow \dfrac1{2x+1}=\dfrac{9}{20}\\\Rightarrow 2x+1=\dfrac{20}{9}\\\Rightarrow 2x=\dfrac{11}{9}\\\Rightarrow x=\dfrac{11}{18}$
