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The value of
21×2×3−22×3×4−⋯−219×20×21−220×21×22\dfrac{2}{1\times2\times3}-\dfrac{2}{2\times3\times4}-\cdots-\dfrac{2}{19\times20\times21}-\dfrac{2}{20\times21\times22}1×2×32−2×3×42−⋯−19×20×212−20×21×222
is mn\dfrac{m}{n}nm where mmm and nnn are co-prime. Find m+nm+nm+n.
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