Question

Answer 1

 

ĐKXĐ:\(x\ne-1\)

\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{x\times\left(x+1\right)}=\dfrac{996}{997}\\ \Rightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{996}{997}\\ \Rightarrow1-\dfrac{1}{x+1}=\dfrac{996}{997}\\ \Rightarrow\dfrac{x+1-1}{x+1}=\dfrac{996}{997}\\ \Rightarrow\dfrac{x}{x+1}=\dfrac{996}{997}\\ \Rightarrow997\left(x+1\right)=996x\\ \Rightarrow997x+997=996x\\ \Rightarrow x+997=0\\ \Rightarrow x=-997\)