Welcome 2016! Part 20

Algebra Level 4

11+2+11+2+3++11+2++20\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 mn \dfrac mn, where mm and nn are coprime positive integers, find the value of m+nm+n.

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