A = 2 + $2^{2}$ +$2^{3}$ + ...............+ $2^{10}$
= ( 2 + $2^{2}$ + ( $2^{3}$ + $2^{4}$ ) + ...................... + ( $2^{9}$ + $2^{10}$ )
= 2 . ( 1 + 2 ) + ........................... + $2^{9}$ . ( 1 + 2 )
= 2 . 3 + .......................................+ $2^{9}$ . 3
= 3 . ( 2 + $2^{9}$ ) chia hết cho 3
⇒ A chia hết cho 3 .