Chứng Minh Rằng : S = 1 + 2 + 2^2 + 2^3 + 2^4 + … + 2^100 chia hết cho 7 , cho 15

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1. S = 1 + 2+ 2^2 + 2^3 + … + 2^100

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

   S = 7 + 2^3(1+2+2^2) + … + 2^98(1+2+2^2)

   S = 7 + 2^3 . 7 + … + 2^98 . 7

   S = 7(1 + 2^3 + … + 2^98) $\vdots$ 7 (đpcm)

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   S = 1 + 2 + 2^2 + 2^3 + … + 2^100

   S = (1 + 2 + 2^2+2^3) + … + (2^97 +2^98 + 2^99 + 2^100)

   S = 15 + … + 2^97(1 + 2 + 2^2 + 2^3)

   S = 15 + … + 2^97 . 15

   S = 15 ( 1 + 2^4 + … + 2^97) $\vdots$ 15 (đpcm)

   $#H$

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