Question

A= 2 la puterea n+3 * 3 la puterea 2n + 2 la puterea n * 9 la puterea n+1 + 2 la puterea n * 3 la puterea 2n+1, n∈IN*
u(A)=?
Explicatie.

Answer 1

   
[tex]a=2^{n+3}\times3^{2n}+2^n\times9^{n+1}+2^n\times3^{2n+1}=\\\\ =2^{n+3}\times (3^2)^n+2^n\times 9^{n+1}+2^n\times(3^2)^n\times3^1=\\\\ =2^n\times2^3\times9^n+2^n\times9^n\times9^1+2^n\times9^n\times 3^1=\\\\ =(2\times9)^n\times2^3+(2\times9)^n\times9^1+(2\times9)^n\times3^1=\\\\ =18^n\times8+18^n\times9+18^n\times3=\\\\ =18^n(8 +9+3)=18^n\times20=\boxed{18^n\times2\times10}\\\\ \texttt{Calculam ultima cifra: } \\ \\ U(18^n \times 2 \times 10) = \boxed{0}~~\text{deoarece unul din factori = 10}[/tex]