Sum it very quickly

Algebra Level 4

\[\large \sum _{n=1}^{2017} \dfrac {n^2 + n - 1}{(n+2)!} = \dfrac 12 - \dfrac a{b!} \]

The equation above holds true for some coprime positive integers \(a\) and \(b\). Find \(a + b\).

\[\] Notation: \(!\) is the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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