An elementary proof of the rationality of $\zeta (2n)/{\pi }^{2n}$

Tom Moshaiov

In $1735$ Euler \cite{1} proved that for each positive integer $k$, the series $\zeta (2k)={\sum }_{\ell =1}^{\infty }{\ell }^{-2k}$ converges to a rational multiple of ${\pi }^{2k}$. Many demons…