9) Ta có
$\underset{n \to +\infty}{\lim} \dfrac{3^n + 6^n - 4^{n+1}}{3^n(1 + 3.2^{n+1})} = \underset{n \to +\infty}{\lim} \dfrac{6^n - 4.4^n + 3^n}{3^n + 6^{n+1}}$
$= \underset{n \to +\infty}{\lim} \dfrac{6^n [1 - 4.(\frac{2}{3})^n + (\frac{1}{2})^n]}{6^n[(\frac{1}{2})^n + 6]}$
$= \underset{n \to +\infty}{\lim} \dfrac{1 - 4.(\frac{2}{3})^n + (\frac{1}{2})^n}{(\frac{1}{2})^n + 6}$
$= \dfrac{1}{6}$
