Đặt $B=1+2+2^2+2^3+2^4+...+2^{2019}$
$⇒2B=2+2^2+2^3+2^4+2^5+...+2^{2020}$
$⇒2B-B=2+2^2+2^3+2^4+2^5+...+2^{2020}-1-2-2^2-2^3-2^4-...-2^{2019}$
$⇔B=2^{2020}-1$
Khi đó $A=\dfrac{B}{1-2^{2020}}=\dfrac{2^{2020}-1}{1-2^{2020}}=\dfrac{-(1-2^{2020})}{1-2^{2020}}=-1$