\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{2003\cdot2004}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2003}-\frac{1}{2004}\)
\(=1-\frac{1}{2004}\)
\(=\frac{2004}{2004}+\frac{-1}{2004}=\frac{2003}{2004}\)
#Hoq chắc _ Baccanngon