\(E=\dfrac{1}{2}\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{19.20}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{19}-\dfrac{1}{20}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{20}\right)\)
\(=\dfrac{1}{2}.\dfrac{19}{20}\)
\(=\dfrac{19}{40}\)