P =2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^10
= ( 2+2^2 ) + ( 2^3 + 2^4 ) + ( 2^5 + 2^6 ) + ( 2^7 + 2^8 ) + ( 2^9 + 2^10 )
= 2.( 1+2 ) + 2^3.( 1+2 ) + 2^5.( 1+2 ) + 2^7.( 1+2 ) + 2^9.( 1 + 2 )
= 2.3+2^3.3+2^5.3+2^7.3+2^9.3
= ( 2+2^3+2^5+2^7+2^9).3 chia hết cho 3
=> P chia hết cho 3