1+2+22+23+...22006
=(1+2+22)+(23+24+25)+....+(22004+22005+22006)
=(1+2+22)+23x(1+2+22)+....+22004x(1+2+22)
=(1+2+22)x(1+23+...+22004)
=7x(1+23+...+22004)
Vì 7x(1+23+...+22004) chia hết cho 7
nên 1+2+22+23+...22006 chia hết cho 7
Vậy 1+2+22+23+...22006 chia hết cho 7