Induction proof of an inequality

1. May 8, 2010

nastygoalie89

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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!

2. May 8, 2010

Cyosis

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

3. May 8, 2010

nastygoalie89

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

4. May 8, 2010

Cyosis

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