Binomial Theorem And Its Simple Applications Question 93
Question: If $ P(n):3^{n}<n!,n\in N, $ then P(n) is true
Options:
A) For $ n\ge 6 $
B) For $ n\ge 7 $
C) For $ n\ge 3 $
D) For all n.
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] Given that, $ P(n):3^{n}<n! $ Now, $ P(7):3^{7}<7! $ is true Let $ P(k):3^{k}<k! $
$ \Rightarrow P(k+1):{3^{k+1}} $
$ ={{3.3}^{k}}<3.k!<(k+1)!(\because k+1>3) $
BETA
