Recursive Formulas - Definition & Examples

The factorial "!" is defined for integers $n$ such that $n! = n(n-1)(n-2) \cdots 1$. For example, $5! = 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 120$.

Find the last $4$ digits of

$$1(1!) + 2(2!) + 3(3!) + \ldots + 2013(2013!).$$

Source: Lexington Math Tournament