Q. The smallest positive integer $n$ for which $n! < \left( \ \frac{n + 1}{2} \right)^{n}$ holds, is
A) 1
B) 2
C) 3
D) 4
Explanation
(b)
Given, $n! < \left( \ \frac{n + 1}{2} \right)^{n}$
At $n = 1$,
$1! \nless 1$
At $n = 2,$
$2! < \left( \frac{3}{2} \right)^{2}$
$\Rightarrow 2 < 2.25$ which is true.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.