Counting on Top, Factorials on Bottom

Algebra Level 3

$\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+\cdots+\dfrac{2015}{2016!}$

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

2!

2017!

2016!

2014!

2

2017

2016

2014