Binomial-Theorem-And-Its-Simple-Applications Question 232
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
Correct Answer: C $ \Rightarrow n!<{{( \frac{n+1}{2} )}^{n}} $ $ \Rightarrow n!<{{( \frac{n+1}{2} )}^{n}} $ $ \therefore $ It is seen that $ n!<{{( \frac{n+1}{2} )}^{n}} $
Show Answer
Answer:
Solution:
When $ n=3, $ then $ n!=6,{{( \frac{n+1}{2} )}^{n}}=8 $
When $ n=4, $ then $ n!=24. $
$ {{( \frac{n+1}{2} )}^{n}}=\frac{625}{16}\Rightarrow n!<{{( \frac{n+1}{2} )}^{n}} $
BETA
