A = $\dfrac{2}{1 × 3}$ + $\dfrac{2}{3 × 5}$ + ... + $\dfrac{2}{2015 × 2017}$ + $\dfrac{2}{2017 × 2019}$
= $\dfrac{1}{1}$ - $\dfrac{1}{3}$ + $\dfrac{1}{3}$ - $\dfrac{1}{5}$ +... + $\dfrac{1}{2015}$ - $\dfrac{1}{2017}$ + $\dfrac{1}{2017}$ - $\dfrac{1}{2019}$
= $\dfrac{1}{1}$ - $\dfrac{1}{2019}$
= $\dfrac{2019 - 1}{2019}$
= $\dfrac{2018}{2019}$