3n+3 + 2n+3 + 3n+1 + 2n+2
= 3n . 33 + 2n . 23 + 3n . 3 + 2n . 22
= 3n . (27 + 3) + 2n . (8 + 4)
= 3n . 30 + 2n . 12
= 3n . 5 . 6 + 2n . 2 . 6
= 6.(3n . 5 + 2n . 2) chia 6 dư 0
Vậy...
=3^n.3^3+2^n.2^3+3^n.3+2^n.2^2
=(3^n.3^3+3^n.3)+(2^n.2^3+2^n.2^2)
=3^n.(3^3+3)+2^n.(2^3+2^2)
=3^n.30+2^n.12
=3^n.5.6+2^n.2.6=6.(3^n.5+2.2^n) chia hết cho 6
Vậy bt chia 6 dư 0
\(3^{n+3}+2^{n+3}+3^{n+1}+2^{n+2}\)
\(=3^2.3^{n+1}+2.2^{n+2}+3^{n+1}+2^{n+2}\)
\(=3^{n+1}.\left(3^2+1\right)+2^{n+2}.\left(2+1\right)=3^{n+1}.2.5+2^{n+2}.3\)
\(=3^n.6.5+2^{n+1}.6=6.\left(5.3^n+2^{n+1}\right)\)
Chia hết cho 6
3n+3+2n+3+3n+1+2n+2 = (3n+3 + 3n+1)+(2n+3+2n+2)
=3n.(33+3)+2n+1(22+2)
=3n.30+2n+1.6
=3n.5.6+2n+1.6
=6.(3n.5+2n+1)
=>3n+3+2n+3+3n+1+2n+2 chia hết cho 6
hay 3n+3+2n+3+3n+1+2n+2 chia 6 dư 0
