\(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{2004.2005.2006}\)
\(=\frac{2}{1.2}-\frac{2}{2.3}+\frac{2}{2.3}-\frac{2}{3.4}+...+\frac{2}{2004.2005}-\frac{2}{2005.2006}\)
\(=\frac{2}{1.2}-\frac{2}{2005.2006}\)
\(=1-\frac{1}{2011015}\)
\(=\frac{2011015}{2011015}-\frac{1}{2011015}\)
\(=\frac{2011014}{2011015}\)
Cbht