An Interesting Product

Algebra Level 4

(114)(119)(1116)(1110000) \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 ab \dfrac ab for coprime positive integers aa and bb, find the value of a+ba+b.

Bonus: Generalize this.

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