Question

Como resolver a questão em Anexo

Answer 1

$\dfrac{20 \cdot (4^{n+1}+4^{n-1})}{17 \cdot (4^{n}+4^{n+1})} = \\\\\\ \dfrac{20 \cdot (4^{n} \cdot 4^{1}+4^{n} \cdot 4^{-1})}{17 \cdot (4^{n}+4^{n} \cdot 4^{1})} = \\\\\\ \dfrac{20 \cdot 4^{n} \cdot 4+20 \cdot 4^{n} \cdot 4^{-1}}{17 \cdot 4^{n}+17 \cdot 4^{n} \cdot 4} = \\\\\\ \dfrac{80 \cdot 4^{n}+20 \cdot 4^{n} \cdot \frac{1}{4}}{17 \cdot 4^{n}+68 \cdot 4^{n}} = \\\\\\ \dfrac{80 \cdot 4^{n}+5 \cdot 4^{n}}{17 \cdot 4^{n}+68 \cdot 4^{n}} = \\\\\\ \dfrac{4^{n} \cdot (80+5)}{4^{n} \cdot (17+68)}=$

$\dfrac{85}{85} = \boxed{1}$

A resposta final é 1.

Answer 2

A resposta está em anexo, espero que te ajude ;)