Question

Aratati ca (2^n+2+2^n)/(4^n+1+4^n)pentru orice n €N

Answer 1

(2^n+2+2^n)/(4^n+1+4^n)=
=(2^n+2+2^n)/(2^2n+2+2^2n)=
=2^n(2²+2⁰)/[2^2n(2²+2⁰)]=
=2^n × 5/2^2n ×5=
=2^n/2^2n=
=2/2²=
=1/2