\[ \left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\ldots\left(1-\frac{1}{999}\right)\left(1-\frac{1}{1000}\right) \]

If the value of the expression above can be expressed as \( \frac ab\) for coprime positive integers \(a\) and \(b\), find the value of \(a+b\).

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