Binomial Theorem And Its Simple Applications Question 183
Question: $ n^{n}{{( \frac{n+1}{2} )}^{2n}} $ is
[AMU 2001]
Options:
A) Less than $ {{( \frac{n+1}{2} )}^{3}} $
B) Greater than $ {{( \frac{n+1}{2} )}^{3}} $
C) Less than $ {{(n!)}^{3}} $
D) Greater than $ {{(n!)}^{3}}, $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ y=n^{n}{{( \frac{n+1}{2} )}^{2n}} $
Put n = 2, $ y=2^{2}{{( \frac{3}{2} )}^{4}}=4,.,\frac{81}{16}=\frac{81}{4}\tilde{-} $ 20
Option (a) $ {{\left( \frac{n+1}{2} \right)}^{3}}=\frac{27}{8}<y $
Option (b) $ ={{( \frac{n+1}{2} )}^{3}}=\frac{27}{8} < y $
Option (c) $ ={{(2!)}^{3}}=8$
Option (d) $ ={{(2!)}^{3}}=8 $ .
BETA
