Question

\(A=1+2+2^2+2^3+...+2^{2019}\)

Answer 1

\(A=1+2+2^2+2^3+...+2^{2019}\\ 2A=2+2^2+2^3+2^4+...+2^{2020}\\ 2A-A=\left(2+2^2+2^3+2^4+...+2^{2020}\right)-\left(1+2+2^2+2^3+...+2^{2019}\right)\\ A=2^{2020}-1\)