Question

[ABC]

C/M rằng : 3ⁿ⁺³+3ⁿ⁺¹+2ⁿ⁺³+2ⁿ⁺² ⋮6 với n∈N*

Answer 1

[Akai Haruma]

Lời giải:

Ta có:
\(A=3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)

\(A=3^{n+1}(3^2+1)+2^{n+2}(2+1)\)

\(A=10.3^{n+1}+3.2^{n+2}\)

\(A=5.6.3^n+6.2^{n+1}=6(5.3^n+2^{n+1})\)

Do đó $A$ chia hết cho $6$

Ta có đpcm.