Question

Exercitiul 1 de la Maramures , ajutoor

Answer 1

$A=36 \cdot 18^{n+1}-2^n \cdot 9^{n+1}-3^{n+2} \cdot 6^n= \\ \\ ~~~=36 \cdot 18 \cdot 18^n-2^n \cdot 9^n \cdot 9-3^2 \cdot 3^n \cdot 6^n= \\ \\ ~~~=648 \cdot 18^n - 18^n \cdot 9-9 \cdot 18^n= \\ \\ ~~~=18^n(648-9-9)= \\ \\ ~~~=18^n \cdot 630= \\ \\ ~~~= 18^n \cdot 2 \cdot \boxed{315 } \Rightarrow A ~ \vdots~315.$

Answer 2

[tex]A=36\cdot 18^{n}\cdot18-2^n\cdot 9^n\cdot 9-3^n\cdot 6^n\cdot 3^2\\ A=18^n(648-9-9)=630\cdot 18^n=315\cdot 2\cdot18^n\ \textgreater \ A\vdots315[/tex]