Question

Aratati ca nr Q=14^(n+1)+2^n*7^(n+2) se divide cu 9, oric are ar fi "n"
Multumesc.

Answer 1

Răspuns:

14×14^n+49×1`4^n=14^n(14+49)=63×14^n

Explicație pas cu pas:

Answer 2

$Q = 14^{n+1}+2^n\cdot 7^{n+2}\\ \\ = (2\cdot 7)^{n+1}+2^n\cdot 7^{n+2}\\ \\=2^{n+1}\cdot 7^{n+1}+2^n\cdot 7^{n+2}\\ \\ = 2^n\cdot 7^{n+1}\cdot (2+7)\\ \\ = 2^n\cdot 7^{n+1}\cdot 9\,\,\vdots\,\, 9\quad \checkmark$