Principle Of Mathematical Induction Question 50
If $ P(n):3^{n}<n!,n\in N, $ then P(n) is not necessarily true
Options:
A) For $ n\ge 6 $
B) For $ n\ge 7 $
C) For $ n\ge 3 $
D) For all integers n.
Correct Answer: B Given that, $ P(n):3^{n}<n! $ Now, $ P(7):3^{7}<7! $ is true Let $ P(k):3^{k}<k! $ be true for some $ k \geq 7 $
$ \Rightarrow P(k+1):{3^{k+1}} $ $ ={3^{k+1}}<3.k!<(k+1)!(\because k+1>3) $
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Answer:
Solution:
BETA
