Bài 3:
\(A=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{15\cdot17}+\dfrac{1}{17\cdot19}\)
\(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{15\cdot17}+\dfrac{2}{17\cdot19}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{15}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{19}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{18}{19}=\dfrac{9}{19}\)