Binomial Theorem And Its Simple Applications Question 75
Question: If $ n\in N $ and $ n>1, $ then
Options:
A) $ n!>{{( \frac{n+1}{2} )}^{n}} $
B) $ n!\ge {{( \frac{n+1}{2} )}^{n}} $
C) $ n!<{{( \frac{n+1}{2} )}^{n}} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] when n =2 then $ {{( \frac{n+1}{2} )}^{n}}=\frac{9}{4} $
$ \Rightarrow n!<{{( \frac{n+1}{2} )}^{n}} $
When $ n=3, $ then $ n!=6,{{( \frac{n+1}{2} )}^{n}}=8 $
$ \Rightarrow n!<{{( \frac{n+1}{2} )}^{n}} $
When $ n=4, $ then $ n!=24. $
$ {{( \frac{n+1}{2} )}^{n}}=\frac{625}{16}\Rightarrow n!<{{( \frac{n+1}{2} )}^{n}} $
$ \therefore $ It is seen that $ n!<{{( \frac{n+1}{2} )}^{n}} $
BETA
