Tìm x biết 1/3+1/6+1/10+...+2/x(x+1)=2013/2014

* Hướng dẫn giải

$\frac{1}{3}$ = $\frac{2}{6}$= $\frac{2}{\left(2x3\right)}$ = $\frac{2}{2}$- 
$\frac{1}{6}$= $\frac{2}{12}$ = $\frac{2}{\left(3x4\right)}$= $\frac{2}{3}$ - 
...
$\frac{2}{x(x+1)}$= $\frac{2}{x}$-$\frac{2}{(x +1)}$
Do đó: 
$\frac{1}{3}$ + $\frac{1}{6}$+ ... + $\frac{2}{x(x+1)}$ = $\frac{2}{2}$ - $\frac{2}{3}$ + $\frac{2}{3}$ - $\frac{2}{4}$+ ... +$\frac{2}{x}$- $\frac{2}{(x + 1)}$ = $\frac{2}{2}$ - $\frac{2}{(x+1)}$
suy ra 1 - $\frac{2}{(x + 1)}$= $\frac{2013}{2014}$

x= 4027