# 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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