A) For \[n\ge 6\]
B) For \[n\ge 7\]
C) For \[n\ge 3\]
D) For all n.
Correct Answer: B
Solution :
[b] Given that, \[P(n):{{3}^{n}}<n!\] Now, \[P(7):{{3}^{7}}<7!\] is true Let \[P(k):{{3}^{k}}<k!\] \[\Rightarrow P(k+1):{{3}^{k+1}}\] \[={{3.3}^{k}}<3.k!<(k+1)!\,\,(\because \,\,\,\,k+1>3)\]
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