Wallis product

Theorem

The following formula holds: $$\displaystyle\prod_{k=1}^{\infty} \left[ \dfrac{2k}{2k-1} \dfrac{2k}{2k+1} \right] = \dfrac{2}{1} \cdot \dfrac{2}{3} \cdot \dfrac{4}{3} \cdot \dfrac{4}{5} \cdot \dfrac{6}{5} \cdot \dfrac{6}{7} \ldots = \dfrac{\pi}{2},$$ where $\pi$ denotes pi.