# Limit using theorems

1. Sep 30, 2007

### Gott_ist_tot

1. The problem statement, all variables and given/known data
Prove using limit theorems that

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

2. Relevant 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) = $$\infty$$

3. 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.

Last edited: Sep 30, 2007
2. Sep 30, 2007

### 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

3. Sep 30, 2007

### Gott_ist_tot

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