# 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 $$m+n$$.

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