Many fractions

Algebra Level 4

$\large \frac{1}{1+2}+ \frac{1}{1+2+3}+\cdots+ \frac{1}{1+2+3+\dots+2016}$

The expression above is in form of $\dfrac{a}{b}$ , where $a$ and $b$ are coprime positive integers, find $a+b$ .