Question

Alguém pode me ajudar ?

Answer 1

$\frac{2^{n+2}+2^{n-1}}{2^{n+1}}$

$2^{n+2}+2^{n-1}$

$=2^2\cdot \:2^n+2^{-1}\cdot \:2^n$

$=2^{-1}\left(8+1\right)\cdot \:2^n$

$=9\cdot \:2^{n-1}$

$\frac{9\cdot \:2^{n-1}}{2^{n+1}}$

$\frac{2^{n-1}}{2^{n+1}}=\frac{1}{2^{\left(n+1\right)-\left(n-1\right)}}=\frac{1}{2^2}$

$=\frac{9}{2^2}$

$=\left(\frac{9}{2^2}\right)^{\frac{1}{2}}$

$=\frac{9^{\frac{1}{2}}}{\left(2^2\right)^{\frac{1}{2}}}$

$=\frac{9^{\frac{1}{2}}}{2}$

$=\frac{3}{2}$

caramba, resposta certa opção "B"

espero ter ajudado