\(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2004.2006}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2004}-\frac{1}{2006}\)
\(=\frac{1}{2}-\frac{1}{2006}\)
\(=\frac{1003}{2006}-\frac{1}{2006}\)
\(=\frac{1002}{2006}\)
\(=\frac{501}{1003}\)