Fun with series 2

Algebra Level 4

The value of

\(\dfrac{2}{1\times2\times3}-\dfrac{2}{2\times3\times4}-\cdots-\dfrac{2}{19\times20\times21}-\dfrac{2}{20\times21\times22}\)

is \(\dfrac{m}{n}\) where \(m\) and \(n\) are co-prime. Find \(m+n\).

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