An Interesting Product

Algebra Level 4

\[ \left( 1 - \frac14\right)\left( 1 - \frac19\right)\left( 1 - \frac1{16}\right)\cdots \left( 1 - \frac1{10000}\right) \]

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

Bonus: Generalize this.

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