Proof with nonnegative integers

[Kasperloeye]

Hey I'm new on this forum.. and I'm a little stuck.. I need to prove what nonnegative integers n makes the following statement

n² <=n! I know the values.. but I'm a little fuzzy on how to do induction-proofs.. anyone who can give a hand or kick me in the right direction??

 

[stapel]

I'm a little fuzzy on how to do induction-proofs.

Then study and learn! :wink:

 

[Kasperloeye]

Re:

I'm a little fuzzy on how to do induction-proofs.

Then study and learn! :wink:

Hehe I know.. but I need a little kick in the right direction.. care to do that.. I don't want you to solve it.. just a small kick

 

[Kasperloeye]

oh.. OOH! .. I think I got it!! ^^

 

[Kasperloeye]

Here goes:
So Basis should be n=4 since
4²<=4!
16 <=24

SO: For n=k, k²<=k!

but if we take it with n= k+1 it's (k+1)² <=(k+1)!
(k+1)² <= (k+1)(k!)
(k+1) <= k!
but our hypothasis says k^2 <= k!, and because k+1 <= k^2 (for k>=4) then
k+1 <= k^2 <= k!.

right??