A simple computation of $\zeta (2k)$ by using Bernoulli polynomials and a telescoping series

Ó. Ciaurri, L. M. Navas, F. J. Ruiz +1

We present a new proof of Euler's formulas for $\zeta (2k)$, where $k=1,2,3,...$, which uses only the defining properties of the Bernoulli polynomials, obtaining the value of $\zeta (2k)$…