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#1 2011-10-26 06:20:06

JohnJ
Member
Registered: 2011-10-26
Posts: 2

Math induction

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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#2 2011-10-26 06:57:28

TheDude
Member
Registered: 2007-10-23
Posts: 361

Re: Math induction

By inspection this is true for n = 0 and n = 1.  Prove it is not true for n >= 2:


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#3 2011-10-26 14:28:14

reconsideryouranswer
Member
Registered: 2011-05-11
Posts: 171

Re: Math induction

JohnJ wrote:

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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I wish a had a more interesting signature line.

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#4 2011-10-27 03:19:43

TheDude
Member
Registered: 2007-10-23
Posts: 361

Re: Math induction

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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