12:
a: \(A=3^{n+3}+3^{n+1}+2_{}^{n+2}+2^{n+1}\)
\(=3^{n}\cdot27+3^{n}\cdot3+2^{n}\cdot4+2^{n}\cdot2\)
\(=3^{n}\cdot30+2^{n}\cdot6=6\left(3^{n}\cdot5+2^{n}\right)\)
=>A⋮6
b: \(B=3^{n+3}-2^{n+3}+3^{n+1}-2^{n+1}\)
\(=3^{n}\cdot27+3^{n}\cdot3-2^{n}\cdot8-2^{n}\cdot2\)
\(=3^{n}\cdot30-2^{n}\cdot10=10\left(3^{n}\cdot3-2^{n}\right)\)
=>B ⋮10
Bài 11:
a: \(A=3^2+6^2+\cdots+30^2\)
\(=3^2\left(1^2+2^2+\cdots+10^2\right)\)
\(=9\cdot385=3465\)
b: \(B=2^3+4^3+\cdots+20^3\)
\(=2^3\cdot\left(1^3+2^3+\cdots+10^3\right)\)
\(=8\cdot3025=24200\)
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