a) \(A⋮3\)
\(A=2^0+2^1+2^2+....+2^{41}\)
\(=\left(2^0\times1+2^0\times2\right)+...+\left(2^{40}\times1+2^{40}\times2\right)\)
\(=2^0\times\left(1+2\right)+....+2^{40}\times\left(1+3\right)\)
\(=2^0\times3+...+2^{40}\times3\)
\(=3.\left(2^0\times...\times2^{40}\right)⋮3\)
Vậy \(A⋮3\)
b) \(A⋮7\)
\(A=2^0+2^1+2^2+...+2^{41}\)
\(=\left(2^0\times1+2^0\times2+2^0\times2^2\right)+...+\left(2^{39}\times1+2^{39}\times2+2^{39}\times2^2\right)\)
\(=2^0\times\left(1+2+2^2\right)+...+2^{39}\times\left(1+2+2^2\right)\)
\(=2^0\times7+...+2^{39}\times7\)
\(=7\times\left(2^0+...+2^{39}\right)⋮7\)
Vậy \(A⋮7\)
Nếu đúng thì k cho mk nhé
