Prove by induction that n! < n^n for all n > 1.
Added by Rosario P.
Step 1
We have 2! = 2 and 2^2 = 4, so 2! < 2^2 is true. Inductive step: Assume that the statement is true for some n > 1, i.e., n! < n^n. We want to show that (n+1)! < (n+1)^(n+1). We have (n+1)! = (n+1)n! and (n+1)^(n+1) = (n+1)^n * (n+1). Since n! < n^n by our Show more…
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