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