\(=2\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{17.19}\right)\)
\(=2\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{17}-\dfrac{1}{19}\right)\)
\(=2\left(\dfrac{1}{3}-\dfrac{1}{19}\right)=2\text{ }\times\dfrac{16}{57}=\dfrac{32}{57}\).