Question

cho S = 1+2+2²+2³+2⁴+2⁵+2⁶+2⁷

chứng tỏ rằng S chia hết cho 3

Answer 1

S = 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7

S = (1+2) + (2^2 + 2^3) + (2^4 + 2^5) + (2^6 + 2^7)

S = (1+2) + 2^2 (1+2) + 2^4 (1+2) + 2^6 (1+2)

S = 3*1 + 2^2 * 3 + 2^4 * 3 + 2^6 * 3

S = 3 * (1 + 2^2 + 2^4 + 2^6)

Vì 3 ⁝ 3

nên 3 * (1 + 2^2 + 2^4 + 2^6) ⁝ 3

Vậy S ⁝ 3

Answer 2

S = 1 + 2 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷

S = (1 + 2) + (2² + 2³) + (2⁴ + 2⁵) + (2⁶ + 2⁷)

S = 1(1 + 2) + 2²(1 + 2) + 2⁴(1 + 2) + 2⁶(1 + 2)

S = (1 . 3) + (2² . 3) + (2⁴ . 3) + (2⁶ . 3)

S = 3 . (1 + 2² + 2⁴ + 2⁶) ⋮ 3

S ⋮ 3