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

Toán Lớp 6: Cho B=1+4+4²+4³+–+4⁵⁸+4⁵⁹ ,hãy chứng tỏ A chia hết cho 5

Toán Lớp 6: Cho B=1+4+4²+4³+……..+4⁵⁸+4⁵⁹ ,hãy chứng tỏ A chia hết cho 5

Comments ( 2 )

  1. B = 1 + 4 + 4^{2} + 4^{3} + … + 4^{58} + 4^{59}
    ⇒ B = (1 + 4) + (4^{2} + 4^{3}) +…+ (4^{58} + 4^{59})
    ⇒ B = (1 + 4) + 4^{2}(1 + 4) + … + 4^{58}(1 + 4)
    ⇒ B = 1 . 5 + 4^{2} . 5 + … + 4^{58} . 5
    ⇒ B = (1 + 4^{2} + … + 4^{58}) . 5
    ⇒ B vdots 5
     

  2. Ta có:
    B = 1 + 4 + 4^2 + 4^3 + … + 4^58 + 4^59
        = 4^0 + 4^1 + 4^2 + 4^3 + … + 4^58 + 4^59
        = (4^0 + 4^1) + (4^2 + 4^3) + … + (4^58 + 4^59)
        = 4^0 xx (1 + 4) + 4^2 xx (1 + 4) + … + 4^58 xx (1 + 4)
        = 4^0 xx 5 + 4^2 xx 5 + … + 4^58 xx 5
        = 5 xx (4^0 + 4^2 + … + 4^58)
    Do đó, B = 5 xx (4^0 + 4^2 + … + 4^58)
    Ta lại thấy: 5 \vdots 5
        => 5 xx (4^0 + 4^2 + … + 4^58) \vdots 5
    Vậy, B \vdots 5 (\text{đpcm})

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