Evaluating product $\prod_{n=2}^\infty\left(1-\frac{1}{n^2}\right)$

Question

I'm reading about infinite products in complex analysis, where there is a theorem like

The product $\prod_{n=1}^\infty\left(1+a_n\right)$ converges absolutely iff the series $\sum_{n=1}^\infty|a_n|$ converges.

Then an exercise is to show that $\prod_{n=2}^\infty\left(1-\dfrac{1}{n^2}\right)=\dfrac{1}{2}$

The theorem above guarantees that the product converges, but what is the method to evaluate its value?

Answer 1

Hint: $$ 1-\frac{1}{n^2} = \frac{n^2-1}{n^2} = \frac{(n+1)(n-1)}{n^2}$$