\(A=4+2^2+...+2^{20}\)
\(A-4=2^2+2^3+...+2^{20}\)
\(2\left(A-4\right)=2\left(2^2+2^3+...+2^{20}\right)\)
\(2\left(A-4\right)=2^3+2^4+...+2^{21}\)
\(2\left(A-4\right)-\left(A-4\right)=\left(2^3+2^4+...+2^{21}\right)-\left(2^2+2^3+...+2^{20}\right)\)
\(A-4=2^{21}-2^2\)
\(A=2^{21}-4+4=2^{21}\)
\(A=4+2^2+2^3+...+2^{19}+2^{20}\)
\(2A=2.\left(4+2^2+2^3+...+2^{19}+2^{20}\right)\)
\(2A=2^2+2^3+2^4+...+2^{20}+2^{21}\)
\(2A-A=\left(2^2+2^3+2^4+...+2^{20}+2^{21}\right)-\left(4+2^2+2^3+...+2^{19}+2^{20}\right)\)
\(\Rightarrow A=2^2+2^3+2^4+...+2^{20}+2^{21}-4-2^2-2^3-...-2^{19}-2^{20}\)
\(A=\left(2^2-2^2\right)+\left(2^3-2^3\right)+\left(2^4-2^4\right)+...+\left(2^{19}-2^{19}\right)+\left(2^{20}-2^{20}\right)+2^{21}-4\)
\(A=0+0+0+...+0+0\)
\(A=2^{21}-4\)
Vậy \(A=2^{21}-4\)