Q. $\lim_{n \rightarrow \infty}\frac{{3.2}^{n + 1} - {4.5}^{n + 1}}{{5.2}^{n} + {7.5}^{n}}\$ is equal to
A) $\frac{3}{5}$
B) $- \frac{4}{7}$
C) $- \frac{20}{7}$
D) 0
Explanation
(c)
$\lim_{n \rightarrow \infty}\frac{{3.2}^{n + 1} - {4.5}^{n + 1}}{{5.2}^{n} + {7.5}^{n}}\$
$= \lim_{n \rightarrow \infty}\frac{5^{n}\left( 6.\left( \frac{2}{5} \right)^{n} - 20 \right)}{5^{n}\left( 5.\left( \frac{2}{5} \right)^{n} + 7 \right)} = - \frac{20}{7}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.