Chứng minh rằng : 2^1+ 2^2+….+2^10 chia hết cho 3

$\begin{array}{l} {2^1} + {2^2} + … + {2^{10}}\\  = \left( {{2^1} + {2^2}} \right) + \left( {{2^3} + {2^4}} \right) + .. + \left( {{2^9} + {2^{10}}} \right)\\  = 2\left( {1 + 2} \right) + {2^3}\left( {1 + 2} \right) + … + {2^9}\left( {1 + 2} \right)\\  = 2.3 + {2^3}.3 + … + {2^9}.3\\  = 3\left( {2 + {2^3} + … + {2^9}} \right) \vdots 3 \end{array}$