Induction proof of an inequality

[nastygoalie89]

Homework Statement

for all integers n>=1, n! <= n^n

Homework Equations

The Attempt at a Solution

Base case: (1)! <= (1)^(1) 1=1 check
Inductive hypothesis: suppose k!<=k^k
P(k+1): (k+1)! <= (k+1)^(k+1)

From here on out I get very confused. Any help would be appreciated!

 

[Cyosis]

Write $(k+1)! \le (k+1)^{k+1}$ in terms of k and k^k.

 

[nastygoalie89]

so it would be k!(k+1) <= (k+1)^k + (k+1) ?

 

[Cyosis]

The right hand side is incorrect, but you're on the right track.