\(=\dfrac{1}{2}\left(\dfrac{2}{2\cdot3\cdot4}+\dfrac{2}{3\cdot4\cdot5}+...+\dfrac{2}{18\cdot19\cdot20}\right)\)
\(=\dfrac{1}{2}\left(\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+\dfrac{1}{3\cdot4}-\dfrac{1}{4\cdot5}+...+\dfrac{1}{18\cdot19}-\dfrac{1}{19\cdot20}\right)\)
\(=\dfrac{1}{2}\left(\dfrac{1}{6}-\dfrac{1}{380}\right)\)
\(=\dfrac{187}{2280}\)