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

Toán Lớp 6: Cho A= 1+2^1+2^2+-+2^100+2^101. Chứng minh A chia hết cho 7.

Tháng Tư 7, 2022 Toán học 2 Comments 0 views

Toán Lớp 6: Cho A= 1+2^1+2^2+….+2^100+2^101. Chứng minh A chia hết cho 7.

Comments ( 2 )

  1. ankim
    ankim
    7 Tháng Tư, 2022 at 3:45 chiều
    Reply
    A = 1 + 2^1 + 2^2 + … + 2^100 + 2^101
    = (1 + 2 + 2^2) + (2^3 + 2^4 + 2^5) + … + (2^99 + 2^100 + 2^101)
    = (1 + 2 +2^2) + 2^2 . (1 + 2 +2^2) + … + 2^99 . (1 + 2 +2^2)
    = (1 + 2 +2^2) . (1 + 2^2 + 2^6 + … + 2^99)
    = 7 . (1 + 2^2 + 2^6 + … + 2^99) \vdots 7
    Vì 7 \vdots 7                     
    -> A \vdots 7 \text{đpcm}

  2. thanoanghha
    thanoanghha
    7 Tháng Tư, 2022 at 3:45 chiều
    Reply
    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 (đpcm)

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

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