Fun with series 2

Algebra Level 4

The value of

21×2×322×3×4219×20×21220×21×22\dfrac{2}{1\times2\times3}-\dfrac{2}{2\times3\times4}-\cdots-\dfrac{2}{19\times20\times21}-\dfrac{2}{20\times21\times22}

is mn\dfrac{m}{n} where mm and nn are co-prime. Find m+nm+n.

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