Ta có: $\frac{1}{2019}$ +2020.$\frac{2018}{2019}$ -2020
=$\frac{1}{2019}$ +2020.($\frac{2018}{2019}$ -1)
=$\frac{1}{2019}$ +2020.$\frac{-1}{2019}$
=$\frac{1}{2019}$ +(-2020).$\frac{1}{2019}$
=$\frac{1}{2019}$.[1+(-2020)]
=$\frac{1}{2019}$.(-2019)
=-1