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Calculus Level 4

\[\prod _{ n=2 }^{ 1986 } \Bigg({ 1-\frac { 1 }{\displaystyle \sum _{ k=0 }^{ n }{ k } } } \Bigg) \]

If the product above equals to \(\frac a b\) for some relatively coprime positive integers \(a,b\), find \(b-a\).

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