CMR : `E = ( 2+2^2+2^3 +…+2^100 ) ` chia hết cho 31

2 bình luận về “CMR : `E = ( 2+2^2+2^3 +…+2^100 ) ` chia hết cho 31”

1. E = 2+2^2+2^3+…+2^[100]

   E = (2+2^2+2^3+2^4+2^5)+…+(2^[96]+2^[97]+2^[98]+2^[99]+2^[100])

   E = 2(1+2+2^2+2^3+2^4)+…+2^[96](1+2+2^2+2^3+2^4)

   E = 2 . 31 + … + 2^[96] . 31

   E = 31(2+2^2+2^3+…+2^[96])

   Đặt a=2+2^2+2^3+…+2^[96]

   => 31a vdots 31

   => 31(2+2^2+2^3+…+2^[96]) vdots 31

   => E vdots 31 (đpcm)

   color[red]text[@BadMood]

    

   Trả lời
2. E=2+2^2+2^3+…+2^100

   E=(2+2^2+2^3+2^4+2^5)+(2^6+2^7+2^8+2^9+2^10)+…+(2^96+2^97+2^98+2^99+2^100)

   E=2(1+2+2^2+2^3+2^4)+2^6(1+2+2^2+2^3+2^4)+…+2^96(1+2+2^2+2^3+2^4)

   E=(1+2+2^2+2^3+2^4)(2+2^6+…+2^96)

   E=31. (2+2^6+…+2^96)

   Vì 31 vdots 31

   => 31. (2+2^6+…+2^96) vdots 31

   =>E vdots 31 

   Trả lời