Use mathematical induction to prove that n 2 < n!, for all integer n ≥ 4.
Added by Santiago P.
Step 1
Clearly, 16 < 24, so the statement holds true for the base case. Inductive hypothesis: Assume that n^2 < n! for some integer k ≥ 4. Inductive step: We need to show that (k+1)^2 < (k+1)!. We have: (k+1)^2 = k^2 + 2k + 1 (k+1)! = (k+1)k! By the inductive Show more…
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