using mathematical induction, show this
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As with structural induction, I’d like you to follow a fairly rigid format in
presenting proofs by weak mathematical induction. Here’s an example.
Claim: For all n ≥ 4, n! > 2
n
.
Proof by weak mathematical induction on n (n ≥ 4).
Basis: 4! = 24 > 16 = 24
.
Induction:
IH: n! > 2
n
NTS: (n + 1)! > 2
n+1
(n + 1)! = n! · (n + 1) (def of !)
> 2n· (n + 1) (IH)
> 2n· 2 (n ≥ 4)
= 2n+1
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