Câu hỏi của Long thần

Question

Chứng Minh : 3 n+3 +3n+1+2n+3+2n+2 chia hết cho 6  n thuộc N

Nguyễn Việt Lâm · Accepted Answer

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

$=3^{n+1}.10+2^{n+2}.3=3^n.3.2.5+2^{n+1}.2.3$

$=3^n.5.6+2^{n+1}.6=\left(3^n.5+2^{n+1}\right).6⋮6$

Vậy $\left(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\right)⋮6$Câu trả lời: $3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}=3^{n+1}\left(3^2+1\right)+2^{n+2}\left(2+1\right)$

$=3^{n+1}.10+2^{n+2}.3=3^n.3.2.5+2^{n+1}.2.3$

$=3^n.5.6+2^{n+1}.6=\left(3^n.5+2^{n+1}\right).6⋮6$

Vậy $\left(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\right)⋮6$

Bài 8: Chia hai lũy thừa cùng cơ số