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Proof WritingHardInduction

Induction · Hard problem

Induction proves (1−14)(1−19)⋯(1−1n2)=n+12n\left(1 - \dfrac14\right)\left(1 - \dfrac19\right)\cdots\left(1 - \dfrac{1}{n^2}\right) = \dfrac{n + 1}{2n} for n≥2n \ge 2. What is the product up to n=50n = 50?