Welcome 2016! Part 20

Algebra Level 4

$\large \dfrac{1}{1+2}+\dfrac{1}{1+2+3}+\cdots+\dfrac{1}{1+2+\cdots+20}$

If the value of the expression above is equal to $\dfrac mn$ , where $m$ and $n$ are coprime positive integers, find the value of $m+n$ .