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.
by
Satyen Nabar