\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+..........+\dfrac{2}{x.\left(x+1\right)}=\dfrac{2014}{2016}\)
\(\Leftrightarrow\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+.............+\dfrac{2}{x\left(x+1\right)}=\dfrac{2014}{2016}\)
\(\Leftrightarrow2\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+.........+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2014}{2016}\)
\(\Leftrightarrow2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+.....+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{2014}{2016}\)
\(\Leftrightarrow2\left(\dfrac{1}{2}-\dfrac{1}{x+1}\right)=\dfrac{2014}{2016}\)
\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{1007}{2016}\)
\(\Leftrightarrow\dfrac{1}{x+1}=\dfrac{1}{2016}\)
\(\Leftrightarrow x+1=2016\)
\(\Leftrightarrow x=2015\left(tm\right)\)
Vậy ...........