Question

Aratati ca pentru orice n natural:
7 | (2^n+2 + 2^n+1 + 2^n ) . Va roogg

Answer 1

$2^{n+2}+2^{n+1}+2^{n}= 2^{n}*( 2^{2}+2+1)=2^{n}*(4+2+1)=7*2^{n}$
=> 7 | $2^{n+2}+2^{n+1}+2^{n}$

Answer 2

2^n+2+2^n+1+2^n=2^n(2²+2¹+1)=2^n+7
7|(2^n+7)
7|7
7|(2^n+2+2^n+1+2^n)