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

Question

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.

Answer 1

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.