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Infinite Products!

Calculus Level 3

For \(x > 1\), define \(\displaystyle f(x) = \prod_{n=2}^{\infty} \left(1 - \dfrac{1}{n^x}\right)\).

Find the value of \(\dfrac{f(6)}{f^2(3)}\).

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by Ariel Gershon

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