# Calculate $\prod_{n=2}^\infty\bigg(1-\frac1{n^2}\bigg)$ [duplicate]

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How do you compute $\prod_{n=2}^\infty\bigg(1-\frac1{n^2}\bigg)$

I have no clue on how to start. Any help would be appreciated.

## marked as duplicate by Simply Beautiful Art, Jaideep Khare, Namaste, lab bhattacharjee, NChJun 1 '17 at 1:36

Hint. This may be seen as a telescoping product using $$1-\frac1{n^2}=\frac{n-1}{n} \cdot \frac{n+1}{n}, \qquad n\ge2.$$ Hope you can finish it.