Bài 4:
\(A=\frac{2}{3.5}+\frac{2}{5.7}+...........+\frac{2}{2005.2007}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+............+\frac{1}{2005}-\frac{1}{2007}\)
\(=\frac{1}{3}-\frac{1}{2007}\)
\(=\frac{669}{2007}-\frac{1}{2007}=\frac{668}{2007}\)
\(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+.....+\frac{2}{4024035}\)
\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+......+\frac{2}{2005.2007}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-.......+\frac{1}{2005}-\frac{1}{2007}\)
\(=\frac{1}{3}-\frac{1}{2007}\)
\(=\frac{668}{2007}\)