\(A=2^{2019}-2^{2018}-2^{2017}-...-2-1\)
\(A=2^{2019}-\left(2^{2018}+2^{2017}+...+2+1\right)=2^{2019}-B\)
Xét \(B=2^{2018}+2^{2017}+...+2+1\)
\(\Rightarrow2B=2^{2019}+2^{2018}+...+2^2+2\)
\(\Rightarrow2B-2^{2019}+1=2^{2018}+2^{2017}+...+2+1\)
\(\Rightarrow2B-2^{2019}+1=B\)
\(\Rightarrow B=2^{2019}-1\)
\(\Rightarrow A=2^{2019}-B=2^{2019}-\left(2^{2019}-1\right)=2^{2019}-2^{2019}+1=1\)
Vậy \(A=1\)
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