# 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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