Toán chứng mink 3^n+3 + 2^n+3 +3^n+1 + 2^n+2 chia hết cho 6 ( n là số dương ) 15/10/2021 By Anna chứng mink 3^n+3 + 2^n+3 +3^n+1 + 2^n+2 chia hết cho 6 ( n là số dương )
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` Trả lời
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 Trả lời
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`
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