Q. If $P(n):3^{n} < n!,\ n \in N$, then $P(n)$ is true
A) For $n \geq 6$
B) For $n \geq 7$
C) For $n \geq 3$
D) For all $n$
Explanation
(b)
Given that, $P(n):3^{n} < n!$
Now, $P(7):3^{7} < 7!$ is true
Let $P(k):\ 3^{k} < k!$
$\Rightarrow P(k + 1):\ 3^{k + 1} = 3 \bullet 3^{k} < 3 \bullet k! < (k + 1)!\ \ (\because k + 1 > 3)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.