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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