A=(2+\(2^2\))+(\(2^3+2^4\))+...+(\(2^9+2^{10}\))
= 2(1+2)+\(2^3\)(1+2)+...+\(2^9\)(1+2)
=2.3+\(2^3\).3+...+\(2^9\).3
=3(2+\(2^3\)+...+\(2^9\))\(⋮\)3
\(\Rightarrow\)A\(⋮\)3
\(A=2+2^2+2^3+...+2^{10}.\)
\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^9+2^{10}\right).\)
\(A=2\left(1+2\right)+2^3\left(1+2\right)+...+2^9\left(1+2\right).\)
\(A=2.3+2^3.3+...+2^9.3.\)
\(A=3\left(2+2^3+...+2^9\right)⋮3\left(đpcm\right).\)
\(A=\left(2+2^2\right)+2^2.\left(2+2^2\right)+...........2^9.\left(2+2^2\right)\\ =6+2^2.6+............+2^9.6\\ =6.\left(1+2^2+...........+2^9\right)\\ 2.3.\left(1+2^2+...........+2^9\right)chiahếtcho3\\ \Rightarrow Achiahetcho3\)
