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 \( a+b\).