Theo bài ra,ta có:
\(xyz=-20\cdot\frac{1}{2}\cdot\frac{1}{5}=-\frac{20}{10}=-2\)
\(\Rightarrow A=-2+\left(-2\right)^2+\left(-2\right)^3+.....+\left(-2\right)^{2019}\)
\(\Rightarrow-2A=\left(-2\right)^2+\left(-2\right)^3+\left(-2\right)^4+....+\left(-2\right)^{2020}\)
\(\Rightarrow-3A=-2^{2020}+2\)
\(\Rightarrow A=\frac{-2^{2020}+2}{-3}\)