Sum of Factorials 
What is the hundreds digit when 2014! + 2013! + ... + 3! + 2! + 1! is expressed as an integer?

I was hoping to find out some sort of pattern by trying the first few factorials, but far as I can see there's none. Also, there seems to be some formula for this, but I'm not really sure if I understand them. How would I solve this? 

Perform the computations modulo $1000$ (no calculator required):
$$\begin{align}1!&\equiv1,\\
2!&\equiv2,\\
3!&\equiv6,\\
4!&\equiv24,\\
5!&\equiv120,\\
6!&\equiv720,\\
7!&\equiv40,\\
8!&\equiv320,\\
9!&\equiv880,\\
10!&\equiv800,\\
11!&\equiv800,\\
12!&\equiv600,\\
13!&\equiv400,\\
14!&\equiv600,\\
15!&\equiv0.
\end{align}$$
Then the sum (easier backward)
$$313.$$
