First slide

Introduction to P.M.I

Question

The smallest positive integer n for which $n! < {(\frac{n + 1}{2})}^{n}$ holds , is

Easy

A

1
B

2
C

3
D

4

Solution

Given $n! < {(\frac{n + 1}{2})}^{n}$
At n=1, $1! < 1$
At n=2, $2! < {(\frac{3}{2})}^{2} \Rightarrow 2 < 2 .25$ which is true.

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