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

Toán Lớp 6: Cho A=2+2^2+2^3+…+2^60.CMR A chia hết cho 3, A chia hết cho 7, A chia hết cho 5

Tháng Tám 10, 2022 Toán học 2 Comments 0 views

Toán Lớp 6: Cho A=2+2^2+2^3+…+2^60.CMR A chia hết cho 3, A chia hết cho 7, A chia hết cho 5

Comments ( 2 )

  1. ngoclanhoa
    ngoclanhoa
    10 Tháng Tám, 2022 at 8:07 sáng
    Reply
    CMR A $\vdots$ 3
    A = 2 + 2^2 + 2^3 + … + 2^60
    = ( 2 + 2^2 ) + ( 2^3 + 2^4 ) + … + ( 2^59 + 2^60 )
    = 2 . ( 1 + 2 ) + 2^3 . ( 1 +2 ) + … + 2^59 . ( 1 + 2 )
    = 2 . 3 + 2^3 . 3 + … + 2^59 . 3
    = 3 . ( 2 + 2^3 + … + 2^59 ) $\vdots$ 3
    CMR A $\vdots$ 7
    A = 2 + 2^2 + 2^3 + … + 2^60
    = ( 2 + 2^2 + 2^3 + 2^4 ) + … + ( 2^57 + 2^58 + 2^59 + 2^60 )
    = 2 . ( 1 + 2 + 4 ) + .. + 2^57 . ( 1 + 2 + 4 )
    = 2 . 7 + … + 2^57 . 7
    = 7 . ( 2 + … +  2^57 ) $\vdots$ 7
    CMR A $\vdots$ 5
    A = 2 + 2^2 + 2^3 + … + 2^60
    = ( 2 + 2^3 + 2^5 + … + 2^59 ) + ( 2^2 + 2^4 + 2^6 + … + 2^60 )
    = [( 2 + 2^3)+ (2^5 + 2^7) + … + (2^57 + 2^59)] + [( 2^2 + 2^4) + (2^6 + 2^8) +…+(2^58 + 2^60)
    = [ 2 . ( 1 + 4 ) + 2^5 . ( 1 + 4 ) + … + 2^57 . ( 1 + 4 )] + [2^2 . ( 1 + 4 ) + 2^6 . ( 1 + 4 ) +…+ 2^58 . ( 1 + 4 )
    = [ 2 . 5 + 2^5 . 5 + .. + 2^57 . 5 ] + [ 2^2 . 5 + 2^6 . 5 +… + 2^58 . 5 ]
    = 5 . ( 2+ 2^5+ .. + 2^57 ) + 5 . ( 2^2+ 2^6 +… + 2^58 ) $\vdots$ 5

  2. lanminhngoc
    lanminhngoc
    10 Tháng Tám, 2022 at 8:06 sáng
    Reply
    A = $2^{}$+$2^{2}$+$2^{3}$ +…+$2^{60}$ 
    =($2^{}$+$2^{2}$)+($2^{3}$+$2^{4}$)+…+($2^{59}$+$2^{60}$) =2(1+2)+$2^{3}$(1+2)+…+$2^{59}$(1+2)
    =(1+2)(2+$2^{3}$+…+$2^{59}$)
    =3.(2+$2^{3}$+…+$2^{59}$) chia hết cho 3
    A=(2+$2^{2}$+$2^{3}$)+…+($2^{58}$+$2^{59}$+$2^{60}$)
    =2(1+2+4)+…+$2^{58}$(1+2+4)
    =7(2+…+$2^{58}$) chia hết cho 7
    A=(2+$2^{2}$+$2^{3}$+$2^{4}$)+…+($2^{57}$+$2^{58}$+$2^{59}$+$2^{60}$)
    =2(1+2+4+8)+…+$2^{57}$(1+2+4+8)
    =15.(2+…+$2^{57}$) chia hết cho 15, chia hết cho 5

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

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