Proof by induction for $\left(1−\frac14\right)\cdot\left(1−\frac19\right)\cdots\left(1−\frac1{n^2}\right)$ for all natural numbers $n$ with $n \ge 2$
Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction