Is my direct proof correct for $ \prod_{i=2}^{n} \left(1- \frac{1}{i^2}\right) =\frac {n+1}{2n} $ good/correct?
show that for any n $\in$ $\Bbb N$ , if n $\ge$ 2, then $\prod_\limits{i=2}^n $ $\left( 1-\frac{1}{i^2}\right)$ = $\frac{n+1}{2n}$