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

Toán Lớp 6: Cho A = 1 + 2 + 2^2 + … + 2^119 CMR A chia hết cho 3 , 7 , 31

Home/ Toán Lớp 6: Cho A = 1 + 2 + 2^2 + … + 2^119 CMR A chia hết cho 3 , 7 , 31

Toán Lớp 6: Cho A = 1 + 2 + 2^2 + … + 2^119 CMR A chia hết cho 3 , 7 , 31

Tháng Tư 22, 2022 Toán học 2 Comments 0 views

Toán Lớp 6: Cho A = 1 + 2 + 2^2 + … + 2^119
CMR A chia hết cho 3 , 7 , 31

Comments ( 2 )

  1. quynhthanhnhu
    quynhthanhnhu
    22 Tháng Tư, 2022 at 12:11 chiều
    Reply
    A = 1 + 2 + 2^2 + … + 2^119
    A = ( 1 + 2 ) + ( 2^2 + 2^3 ) + … + ( 2^118 + 2 ^119 )
    A = 3 + 2^2 ( 1 + 2 ) + … + 2^118 ( 1 + 2 )
    A = 3 + 2^2 . 3 + …. + 2^118 . 3
    A = 3 ( 1 + 2^2 + … + 2^118 ) \vdots 3
    ⇒ A \vdots 3
    A = 1 + 2 + 2^2 + … + 2^119
    A = ( 1 + 2 + 2^2 ) + ( 2^3 + 2^4 + 2^5 ) + … + ( 2^117 + 2^118 + 2^119 )
    A = 7 + 2^3 ( 1 + 2 + 2^2 ) + … + 2^117 ( 1 + 2 + 2^2 )
    A = 7 + 2^3 . 7 + … + 2^117 . 7
    A = 7 ( 1 + 2^3 + … + 2^117 ) \vdots 7
    ⇒ A \vdots 7
    A = 1 + 2 + 2^2 + … +  2^119
    A = ( 1 + 2 +  2^2 + 2^3 + 2^4 ) + … + ( 2^115 + 2^116 + 2^117 + 2^118 + 2^119 )
    A = 31 + … + 2^115 ( 1 + 2 + 2^2 + 2^3 + 2^4 )
    A = 31 + … + 2^115 . 31
    A = 31 ( 1 + … + 2^115 ) \vdots 31
    ⇒ A \vdots 31
     

  2. diepbich93
    diepbich93
    22 Tháng Tư, 2022 at 12:11 chiều
    Reply
    A = 1+2+2^2+…+2^119
    => A = (1+2) +(2^2 +2^3) + .. +(2^116 +2^117) + (2^118 + 2^119)
    => A =3 + 2^2(1+ 2) + …+ 2^116(1+2)+2^118(1+2)
    => A = 3 + 2^2 . 3 + … + 2^116 . 3 +2^118 . 3
    => A =3(1+2^2 + … +2^116 +2^118) \vdots 3 (đpcm)
    $\\$
    A = 1+2+2^2+…+2^119
    =>A =(1 +2+2^2) + (2^3+2^4+2^5) + … + (2^117 +2^118+2^119)
    => A = 7+ 2^3(1 +2+2^2) + … 2^117(1 +2+2^2)
    =>A = 7 +2^3 . 7 + … +2^117 . 7
    => A = 7(1+2^3 + … 2^117) \vdots 7 (đpcm).
    $\\$
    A = 1+2+2^2+…+2^119
    =>A = (1 +2 + 2^2 + 2^3 +2^4)   + ( +2^5 +2^6 + 2^7 +2^8 +2^9) + … + (2^115 + 2^116 +2^117 +2^118 +2^119)
    =>A = 31 + 2^5(1 +2 + 2^2 + 2^3 +2^4)  + … +2^115(1 +2 + 2^2 + 2^3 +2^4)
    =>A =31 +2^5 . 31 + … + 2^115.31
    =>A =31(1+2^5 + … +2^115) \vdots 31 (đpcm).

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

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