\(A=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{2019}\left(1+2\right)\\ A=3\left(2+2^3+...+2^{2019}\right)⋮3\)
\(A=2+2^2+2^3+...+2^{2020}\)
\(=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{2019}\left(1+2\right)\)
\(=2.3+2^3.3+...+2^{2019}.3\)
\(=3\left(2+2^3+...+2^{2019}\right)⋮3\)
\(A=2\cdot\left(1+2\right)+...+2^{2019}\left(1+2\right)\)
\(=3\cdot\left(2+...+2^{2019}\right)⋮3\)