(1/2-1).(1/3-1).(1/4-1)………(1/2019-1)

\(A=\left({\dfrac{1}{2}-1}\right)\left({\dfrac{1}{3}-1}\right)\left({\dfrac{1}{4}-1}\right)…\left({\dfrac{1}{2019}-1}\right)\)

\(=\left({\dfrac{-1}{2}}\right)\left({\dfrac{-2}{3}}\right)\left({\dfrac{-3}{4}}\right)…\left({\dfrac{-2018}{2019}}\right)\)

\(={(-1)}^{2018}\dfrac{1}{2019}\)

\(=\dfrac{1}{2019}\)