Question

Câu hỏi 1 : chứng minh tổng S = 2 + 2^{2 +} 2³ + 2⁴ + 2⁵   + 2^{6 +} 2^{7 +} 2⁸    chia hết ( - 6 )

Answer 1

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

\(=6.2^0+6.2^2+6.2^4+6.2^6=6.\left(2^0+2^2+2^4+2^8\right)\)

Chia hết cho 6

Answer 2

=> S = ( 2 + 2² ) + ( 2³ + 2⁴ ) + ( 2⁵ + 2⁶ ) + ( 2⁷ + 2^{8 )}

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

=> S = 1.( 2 + 4 ) + 2².( 2 + 4 ) + 2⁴.( 2 + 4 ) + 2⁶.( 2 + 4 )

=> S = 1.6 + 2².6 + 2⁴.6 + 2⁶.6

=> S = 6.( 1 + 2² + 2⁴ + 2⁶ )

Vì 6 ⋮ ( - 6 ) nên 6.( 1 + 2² + 2⁴ + 2⁶ ) ⋮ ( - 6 )

Vậy S ⋮ ( - 6 ) ( đpcm )