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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