Đặt \(A=\frac{3}{3\cdot6}+\frac{3}{6\cdot9}+\frac{3}{9\cdot12}+...+\frac{3}{96\cdot99}\)
\(\Rightarrow A=\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{96}-\frac{1}{99}\)
\(\Rightarrow A=\frac{1}{3}-\frac{1}{99}\)
\(\Rightarrow A=\frac{32}{99}\)
\(\frac{3}{3.6}+\frac{3}{6.9}+\frac{3}{9.12}+...+\frac{3}{96.99}\)
\(=\frac{3}{3}.\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{96}-\frac{1}{99}\right)\)
\(=1.\left(\frac{1}{3}-\frac{1}{99}\right)\)
\(=1.\frac{32}{99}\)
\(=\frac{32}{99}\)
