Factorial sum!

Algebra Level 4

$\large \zeta = \sum_{r=1}^{2016} \dfrac{r^2-r-1}{(r+1)!}$

If $$\zeta$$ can be expressed as $$-\dfrac1{a(b!)}$$, where $$a$$ and $$b$$ are positive integers, find $$a+b$$.

Notation:

$$!$$ denotes the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

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