\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x}+\dfrac{1}{x+1}=\)\(\dfrac{2001}{4006}\)
\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2001}{4006}\)
\(\dfrac{1}{2}-\dfrac{1}{x+1}\) \(=\dfrac{1}{2}-\dfrac{2001}{4006}\)
\(\dfrac{1}{x+1}\) \(=\dfrac{1}{2003}\)
⇔ \(x+1=2003\)
\(x\) \(=2003-1\)
\(x\) \(=2002\)