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

Toán Lớp 6: 7. Cho A = 2 + 2^2+ 2^3+ 2^4 …+ 2^12 . Chứng minh rằng: A chia hết cho 7. Vote 5sao

Tháng Bảy 16, 2022 Toán học 2 Comments 0 views

Toán Lớp 6: 7. Cho A = 2 + 2^2+ 2^3+ 2^4 …+ 2^12 . Chứng minh rằng: A chia hết cho 7.
Vote 5sao

Comments ( 2 )

  1. hatuanlan
    hatuanlan
    16 Tháng Bảy, 2022 at 2:07 chiều
    Reply
    ~ gửi bạn ~
    A = 2 + 2^2+ 2^3+ 2^4 …+ 2^12
        =(2+2^2+2^3)+(2^4+2^5+2^6)+…+(2^10+2^11+2^12)
        =2*(1+2+4)+2^4*(1+2+4)+….+2^10*(1+2+4)
        =(2+2^4+2^7+2^10)*(1+2+4)
        =(2+2^4+2^7+2^10)*7
    Vì 7 ⋮ 7
    => (2+2^4+2^7+2^10)*7 ⋮ 7
    => A ⋮ 7

  2. lantrungbach
    lantrungbach
    16 Tháng Bảy, 2022 at 2:07 chiều
    Reply
    A = 2 + 2^2+ 2^3+ 2^4 …+ 2^12
    A=(2+2^2+2^3)+(2^4+2^5+2^6)+…+(2^10+2^11+2^12)
    A=2×(1+2+4)+2^4×(1+2+4)+….+2^10×(1+2+4)
    A=(2+2^4+2^7+2^10)×(1+2+4)
    A=(2+2^4+2^7+2^10)×7$\vdots$7
    =>A$\vdots$7(ĐPCM)

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

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