# Fun with series 3

Algebra Level 4

$\large 1 - \dfrac1{1+2} - \dfrac1{1+2+3} - \ldots - \dfrac1{1+2+3+\ldots+50}$

If the value of the expression above equals to $$\dfrac mn$$ for coprime positive integers $$m$$ and $$n$$, find the value of $$m+n$$.

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