\(A=2+2^2+2^3+2^4+...+2^{19}+2^{20}\)
\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{19}+2^{20}\right)\)
\(A=6+6\cdot2^2+...+6\cdot2^{18}\)
\(A=6\cdot\left(1+2^2+...+2^{18}\right)⋮\text{ }3\text{ v}\)
\(A=2+2^2+2^3+....+2^{20}.\)
\(=2.\left(1+2\right)+2^3.\left(1+2\right)+...+2^{19}.\left(1+2\right)\)
\(=2.3+2^3.3+...+2^{19}.3\)
\(=3.\left(2+2^3+...+2^{19}\right)⋮3\)
\(\Rightarrow A⋮3\)( đpcm)
\(\text{Vì A có các hạng tử đều là lũy thừa của 2 nên }\) \(A⋮2\)
Vì \(A⋮2\)và \(A⋮3\)Nên \(A⋮6\)(đpcm)
\(A=2+2^2+2^3+....+2^{20}\)
\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{19}+2^{20}\right)\)
\(A=2.\left(1+2\right)+2^3.\left(1+2\right)+...+2^{19}.\left(1+2\right)\)
\(A=2.3+2^3.3+....+2^{19}.3\)
\(=>...\)