Chứng minh rằng :2 +1 + 2² + 2³ + ... + $2^{7}$ chia hết cho 3
2 +1 + 2² + 2³ + ... + $2^{7}$
= 1 + 2+ 2² + 2³ + ... + $2^{7}$
= (1+2) + 2².(1+2) + 2³ . (1+2)+...+ $2^{6}$ . (1+2)
=3+ 2² . 3 + 2³ . 3 +.... + $2^{6}$ . 3
Mà 3 ⋮3 ;2² ⋮ 3 ; 2³ ⋮ 3;...
=> 2 +1 + 2² + 2³ + ... + $2^{7}$ ⋮ 3