\(A=4+2^2+2^3+...+2^{20}\)
\(2A=8+2^3+2^4+...+2^{21}\)
\(A=2A-A=2^{21}\)
Gọi \(2^2+2^3+...+2^{20}\) là A
Ta có: \(A=2^2+2^3+...+2^{20}\)
\(\Rightarrow2A=2^3+2^4+...+2^{21}\)
\(\Rightarrow2A-A=\left(2^3+2^4+...+2^{21}\right)-\left(2^2+2^3+...+2^{20}\right)\)
\(\Rightarrow A=2^{21}-2^2\)
\(\Rightarrow4+2^2+2^3+...+2^{20}=4+2^{21}+2^2=4+2^{21}+4=8+2^{21}\)