Câu hỏi của Nguyễn Lan Kim Anh

Question

CMR:3n+3+3n+1+2n+3+2n+2chia hết cho 6

Nguyễn Ngọc Anh Minh · Accepted Answer

$=3^3.3^n+3.3^n+2^3.2^n+2^2.2^n=$

$=3^n\left(3^3+3\right)+2^n\left(2^3+2^2\right)=30.3^n+12.2^n=$

$=6\left(5.3^n+2.2^n\right)⋮6$Câu trả lời: $=3^3.3^n+3.3^n+2^3.2^n+2^2.2^n=$

$=3^n\left(3^3+3\right)+2^n\left(2^3+2^2\right)=30.3^n+12.2^n=$

$=6\left(5.3^n+2.2^n\right)⋮6$

Nguyễn Đức Trí · Answer

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

$=3^{n+1}\left(9+3\right)+2^{n+2}\left(8+4\right)$

$=12.3^{n+1}+12.2^{n+2}=12.\left(3^{n+1}+2^{n+2}\right)$

mà 12⋮6

$\Rightarrow12.\left(3^{n+1}+2^{n+2}\right)⋮6\Rightarrow dpcm$Câu trả lời: $3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}$

$=3^{n+1}\left(9+3\right)+2^{n+2}\left(8+4\right)$

$=12.3^{n+1}+12.2^{n+2}=12.\left(3^{n+1}+2^{n+2}\right)$

mà 12⋮6

$\Rightarrow12.\left(3^{n+1}+2^{n+2}\right)⋮6\Rightarrow dpcm$