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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 7: `A= 1+2^1+2^2+-+2^100+2^101`. Chứng minh A chia hết cho `7`

Toán Lớp 7: A= 1+2^1+2^2+….+2^100+2^101. Chứng minh A chia hết cho 7

Comments ( 2 )

  1. A = 1 + 2^1 + 2^2 + … + 2^100 + 2^101
    A=(1 + 2 + 2^2) + (2^3 + 2^4 + 2^5) + … + (2^99 + 2^100 + 2^101)
    A=(1 + 2 +2^2) + 2^2 . (1 + 2 +2^2) + … + 2^99 . (1 + 2 +2^2)
    A=(1 + 2 +2^2) . (1 + 2^2 + 2^6 + … + 2^99)
    A=7 . (1 + 2^2 + 2^6 + … + 2^99) \vdots 7                 
    ->A \vdots 7

  2. Giải đáp + Lời giải và giải thích chi tiết:
    A=1+2^1+2^2+…+2^100+2^101
    A=(1+2^1+2^2)+…+(2^99+2^100+2^101)
    A=1.(1+2^1+2^2)+…+2^99.(1+2^1+2^2)
    A=1.7+…+2^{99}.7
    A=(1+…+2^99).7
    Ta thấy 7 $\vdots$ 7
    ⇒  A $\vdots$ 7
    @Wee

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222-9+11+12:2*14+14 = ? ( )

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