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

Toán Lớp 6: Cho `A = 2 + 2^2 + 2^3 + – + 2^99 + 2^100` . CMR A chia hết cho 6

Home/ Toán Lớp 6: Cho `A = 2 + 2^2 + 2^3 + – + 2^99 + 2^100` . CMR A chia hết cho 6

Toán Lớp 6: Cho `A = 2 + 2^2 + 2^3 + – + 2^99 + 2^100` . CMR A chia hết cho 6

Tháng Một 14, 2023 Toán học 2 Comments 0 views

Toán Lớp 6: Cho A = 2 + 2^2 + 2^3 + …. + 2^99 + 2^100 . CMR A chia hết cho 6

Comments ( 2 )

  1. giahan44
    giahan44
    14 Tháng Một, 2023 at 11:31 sáng
    Reply
    $\text{ A = 2 + $2^2$ + $2^3$ + … + + $2^9$$ ^9$ + $2^1$$ ^0$$ ^0$ }$
    $\text{ A = ( 2 + $2^2$ ) + ( $2^3$ + $2^4$ ) + … + ( $2^9$$ ^9$ + + $2^1$$ ^0$$ ^0$ ) }$
    $\text{ A = ( 2 + $2^2$ ) + $2^2$. ( 2 + $2^2$ ) + … + $2^9$$ ^8$. ( 2 + $2^2$ ) }$
    $\text{ A = 6 + $2^2$. 6 + … + $2^9$$ ^8$. 6 }$
    $\text{ A = 6. ( 1 + $2^2$ + … + $2^9$$ ^8$ ) $\vdots$ 6         ( đpcm ) }$
     

  2. tuyetanhthu
    tuyetanhthu
    14 Tháng Một, 2023 at 11:30 sáng
    Reply
    A = 2 + 2^2 + 2^3 + …. + 2^{99} + 2^{100}
    => A = ( 2 + 2^2 )  + ( 2^3 + 2^4 ) + ( 2^5 + 2^6 ) + …. + ( 2^{97} + 2^{98} ) + ( 2^{99} + 2^{100} )
    => A = 6 . 1+ 2^2 . ( 2 + 2^2 ) + 2^4 . ( 2 + 2^2 ) + …. + 2^{96} . ( 2 + 2^2 ) + 2^{98} . ( 2 + 2^2 )
    => A = 6 . 1 + 6 . 2^2 + 6 . 2^4 + …. + 6 . 2^{96} + 6 .  2^{98}
    => A = 6 . ( 1 + 2^2 + 2^4 + … + 2^{96} + 2^{98} )
    => A $\vdots$ 6
    Vậy: A $\vdots$ 6
     

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

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