chứng mink 3^n+3 + 2^n+3 +3^n+1 + 2^n+2 chia hết cho 6 ( n là số dương )

Question

chứng mink 3^n+3 + 2^n+3 +3^n+1 + 2^n+2 chia hết cho 6 ( n là số dương )

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Anna 2 tháng 2021-10-15T11:46:46+00:00 2 Answers 3 views 0

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    0
    2021-10-15T11:47:49+00:00

    Đáp án + Giải thích các bước giải:

    `3^{n+3}+2^{n+3}+3^{n+1}+2^{n+2}`

    `=(3^{n+1}+3^{n+3})+(2^{n+2}+2^{n+3})`

    `=3^{n}(3+3^{3})+2^{n+1}(2+2^{2})`

    `=3^{n}.30+2^{n+1}.6`

    Vì $\left\{\begin{matrix}3^{n}.30 \vdots 6& \\2^{n+1}.6\vdots6& \end{matrix}\right.$

    `→3^{n}.30+2^{n+1}.6` $\vdots$ `6`

    `->` `3^{n+3}+2^{n+3}+3^{n+1}+2^{n+2}` $\vdots$ `6`

    Vậy `3^{n+3}+2^{n+3}+3^{n+1}+2^{n+2}` $\vdots$ `6`

    0
    2021-10-15T11:48:08+00:00

    3^n+3+3^n+1+2^n+3+2^n+2

    = 3^n.27+ 3^n.3 + 2^n.8 +2 ^n .4

    = 3^n ( 27+3)+2^n (8+4)

    = 3^n.30+2^n.12 chia hết cho 6

     

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