\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{x\left(x+1\right)}=\frac{996}{997}\)
\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{996}{997}\)
\(1-\frac{1}{x+1}=\frac{996}{997}\)
\(\frac{1}{x+1}=1-\frac{996}{997}=\frac{1}{997}\)
\(\Rightarrow x+1=997\Rightarrow x=996\)
Vậy \(x=996\)