S = 1 + 2 + 2^2 + 2^3 + 2^4 + … + 2^100 chia hết cho 7

2 bình luận về “S = 1 + 2 + 2^2 + 2^3 + 2^4 + … + 2^100 chia hết cho 7”

1. S = 1 + 2 + 2^2 + 2^3 + 2^4  +2^5+… + 2^98+2^99 +2^100

   =(1 + 2 + 2^2) + (2^3 + 2^4  +2^5)+… + (2^98+2^99 +2^100)

   =(1+2+2^2)+2^3(1+2+2^2)+…+2^98(1+2+2^2)

   =(1+2+2^2)+(1+2^3+…+2^98)

   =7(1+2^3+…+2^98)vdots7

   Trả lời
2. S = 1 + 2 + 2^2 + 2^3 + 2^4 + … + 2^100 chia hết cho 7

   S= (1+2+2^2) + (2^2+2^3+2^4)+…+(2^98+2^99+2^100)

   S= 7+2^2(1+2+2^2)+…+2^98(1+2+2^2)

   S= 7+2^2.7+…+2^98.7

   S=7(1+2^2+…+2^98)

   Vậy S chia hết cho 7

    

   Trả lời