Nhanh lên mình đang cần gấp lắm
Gấp lắm hả :V
\(A=\frac{3}{1\cdot3}+\frac{3}{3\cdot5}+\frac{3}{5\cdot7}+....+\frac{3}{2001\cdot2003}\)
\(=\frac{3}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.....+\frac{1}{2001}-\frac{1}{2003}\right)\)
\(=\frac{3}{2}\left(1-\frac{1}{2003}\right)=\frac{6006}{4006}\)