Is this a legitimate proof by induction?

From: Neil L. (imstr8trippin_at_yahoo.com)
Date: 10/31/04 

Date: Sat, 30 Oct 2004 20:47:16 -0400

Prove for all integers n: 2n + 4 <= (n + 2)!

1. For n = 1, 2(1) + 4 = 6 and (1 + 2)! = 6. Therefore, this formula is
valid for n = 1.
2. For n = 2, 2(2) + 4 = 8 and (2 + 2)! = 24. Therefore, this is valid for
n = 2.
3. Assume n = k, 2k + 4 <= (k + 2)!. Prove that, 2(k+1) + 4 <= (k + 3)!

R.S. = (k + 3)! = (k + 3)(k + 2)!
(k + 3)(k + 2)! >= (k + 3)(2k + 4)
(k + 3)(2k + 4) = 2k^2 + 10k + 12
2k^2 + 10k + 12 >= 10k + 12
10k + 12 >= 2k + 6
2k + 6 = 2(k + 1) + 4

?????????? This induction stuff is new to me, so any help/advice would be
appreciated! Please point out anything I've done wrong/right. Thanks!

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