Counting on Top, Factorials on Bottom

Algebra Level 3

12!+23!+34!++20152016!\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+\cdots+\dfrac{2015}{2016!}

If the value of above expression is in the form 11a1-\dfrac{1}{a}, find aa.

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