Fourier Analysis and the closed form for the Zeta Function at even positive integers

Abstract

Using a summation identity obtained for the Fourier coefficients of $x^{2k}$, we derive a closed form expression for the zeta function at even positive integers, using a technique similar to one in an existing proof by Aladdi and Defant[1], but in a simpler and shorter way.

6 pages, no figures. Comments welcome