[tex]x(1+2+3+\ldots +100)=(-1+2)+(-3+4)+\ldots +(-201+202)[/tex]
[tex]x\cdot\displaystyle\frac{(1+100)\cdot 100}{2}=\underbrace{1+1+\ldots +1}_{\mbox{101 ori}}[/tex]
[tex]50\cdot 101x=101\Rightarrow 50x=1\Rightarrow x=\displaystyle\frac{1}{50}\in\mathbb{Q}[/tex]
