Đáp án:
$x=\dfrac{-3999}{2}$
Giải thích các bước giải:
$x+\dfrac{2}{1.5}+\dfrac{2}{5.9}\ \!\!+\! \ \!.\!.\!.+\ \dfrac{2}{101.105}=-1999\dfrac{1}{210}\\\Rightarrow2x+\dfrac{4}{1.5}+\dfrac{4}{5.9}\ \!\!+\! \ \!.\!.\!.+\ \dfrac{4}{101.105}=-3998\dfrac{1}{105}\\\Rightarrow2x+1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}\ \!\!+\! \ \!.\!.\!.+\ \dfrac{1}{101}-\dfrac{1}{105}=-3998\dfrac{1}{105}\\\Rightarrow2x+1-\dfrac{1}{105}=-3998\dfrac{1}{105}\\\Rightarrow2x+\dfrac{104}{105}=-3998\dfrac{1}{105}\\\Rightarrow2x=-3999\\\Rightarrow x=\dfrac{-3999}{2}$
Vậy $x=\dfrac{-3999}{2}$.
