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Hi folks,
Gotta solve this one as well. Any help appreciated.
For which non-negative integers is n² ≤ n!? Answer to be proven with math induction.
regards
John J
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By inspection this is true for n = 0 and n = 1. Prove it is not true for n >= 2:
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Hi folks,
Gotta solve this one as well. Any help appreciated.
For which non-negative integers is
n² ≤ n! ?Answer to be proven with math induction.
regards
John J
User TheDude, there is a factorial sign in that exercise.
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Whoops, thanks for the catch. Ok, so starting over, by inspection we can see that n^2 <= n! is true for n = 0,1 and false for n = 2,3. Prove that it is true for n >= 4:
So whenever n+1 <= n! and the original inequality holds for n, then by induction it holds for n+1. Now do another induction to show that n+1 <= n! for all n >= 4 and you're done.
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