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Show that n factorial is greater than or equals to 2 the power of n for n greater than or equal to 4?
Wiki User
∙ 14y ago
For n = 4,
4! = 4*3*2*1 = 24 and 24 = 2*2*2*2 = 16
So the statement is true for n = 4.
Suppose it is true for n = k, that is, k! > 2k
Then (k+1)! = (k+1)*k!
> (k+1)*2k (since k! > 2k)
> 2*2k (since k >= 4 > 2)
= 2k+1
So if the statement is true for n = k then it must be true for n = k+1. Therefore, since it is true for n = 4 it must be true for all n > 4.
Wiki User
∙ 14y ago
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