lim $\frac{3.4^{n} - 3^{n}}{-4^{n} + 1}$
= lim $\frac{3.(\frac{4^{n}}{4^{n}} - (\frac{3}{4})^{n}}{-(\frac{4}{4})^{n} + \frac{1}{4^{n}} }$
= lim $\frac{3.1 - (\frac{3}{4})^{n}}{-1^{n} + \frac{1}{4^{n}}}$
= $\frac{3}{-1}$
= -3
Vậy lim $\frac{3.4^{n} - 3^{n}}{-4^{n} + 1}$ = -3.