Question

Chứng minh S=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8 chia hết cho -6

Answer 1

S=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8

S=(2+2^2)+(2^3+2^4)+(2^5+2^6)+(2^7+2^8)

S=6+2^2(2+2^2)+2^4(2+2^2)+2^6(2+2^2)

S=6+2^2.6+2^4.6+2^6.6

S=6(1+2^2+2^4+2^6)=>S chia hết cho -6

Answer 2

S=2+2²+2³+2⁴+2⁵+2⁶+2⁷+2⁸=(2+2²)+2²(2+2²)+2⁴(2+2²)+2⁶(2+2²)

S=6+4x6+16x6+64x6

Vì 6 chia hết 6 nên 4x6 chia hết 6 ,16x6 chia hết 6, 64x6 chia hết 6

nên 6+4x6+16x6+64x6 chia hết 6

Vậy 2+2²+2³+2⁴+2⁵+2⁶+2⁷+2⁸ chia hết cho 6