\(\frac{1}{2002}+\frac{2003.2001}{2002}-2003\)
\(=\frac{1}{2002}+\frac{2003.3001}{2002}-\frac{2003.2002}{2002}\)
\(=\frac{1}{2002}+\frac{2003.2001-2003.2002}{2002}\)
\(=\frac{1}{2002}+\frac{-2003}{2002}=\frac{1+\left(-2003\right)}{2002}=\frac{-2002}{2002}=-1\)