Proving lim 10^n/n!=0 Using Limit Theorems

[Gott_ist_tot]

Homework Statement

Prove using limit theorems that

$$lim \frac{10^n}{n!} = 0$$

Homework Equations

We get to use limit theorems. These include
1 lim(a+b) = lim a + lim b,
2 lim(ab) = lim(a)lim(b),
3 lim(s_n) = $$\infty$$ iff lim(1/s_n)= 0,
4 lim(ks_n) = k*lim(s_n)
5 if lim(s_n) = $$\infty$$ and lim(t_n) equals some real number, then lim(s_n*t_n) = $$\infty$$

The Attempt at a Solution

I am having difficulty figuring out how to manipulate the factorial to match a theorem. Any advice/hints would be appreciated. Thanks.

 

[rock.freak667]

What does the limit approach? (n---> ?) well expand out n! as n(n-1)(n-2)*...*3*2*1 and see if that helps

 

[Gott_ist_tot]

n approached infinity. But what you said did it. Thanks.