Ta có:\(A=2+2^2+........+2^{2011}\)
\(=\left(2+2^2+2^3\right)+.............\left(2^{2008}+2^{2009}+2^{2010}\right)+2^{2011}\)
\(=2\left(1+2+2^2\right)+..........+2^{2008}\left(1+2+2^2\right)+2^{2011}\)
\(=2.7+2^4.7+..............+2^{2008}.7+2^{2011}\) không chia hết cho 7