The Riemann and Hurwitz zeta functions, Apery’s constant and new rational series involving $\zeta(2k)$

n this talk, we discuss about some new "fast converging" series representations for Apery's constant and series representations involving $\zeta(2k)$ and binomial coefficients using ideas from the previous talk. One of the main ingredients used in the derivation of such representations is the Clausen acceleration formula as well as power series of trigonometric functions. In particular cases, we recover some well-known series representations of $\pi$. (joint work with Derek Orr)