$P = \dfrac{1}{1 \times 2} + \dfrac{1}{2 \times 3} + \dfrac{1}{3 \times 4} + .... + \dfrac{1}{2018 \times 2019}$
$P =\dfrac{1}{1} - \dfrac{1}{2} + \dfrac{1}{2} -\dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{4} + ... + \dfrac{1}{2018} -\dfrac{1}{2019}$
$P = 1 - \dfrac{1}{2019}$
$P = \dfrac{2018}{2019}$