Question

$\lim\limits_{n \to \infty} \frac{3.2^{n+1}-4.5^{n+1} } {5.2^n+7.5^n}$ =

• A. $0$
• B. $\frac {3}{5}$
• C. $\frac {-4}{7}$
• D. $\frac {-20}{7}$

Answer 1

Answer: (D)

$\displaystyle\lim _{n \rightarrow \infty} \frac{3 \cdot 2^{n+1}-4 \cdot 5^{n+1}}{5 \cdot 2^{n}+7 \cdot 5^{n}}$
$=\displaystyle\lim _{n \rightarrow \infty} \frac{5^{n}\left(6 \cdot\left(\frac{2}{5}\right)^{n}-20\right)}{5^{n}\left(5 \cdot\left(\frac{2}{5}\right)^{n}+7\right)} $
$= -\frac{20}{7} $