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In a recent work on Euler-type formulae for even Dirichlet beta values, i.e.$\beta{(2n)}$, I have derived an exact closed-form expression for a class ofzeta series. From this result, I have conjectured closed-form summations fortwo families of zeta series. Here in this work, I begin by using a knownformula by Wilton to prove those conjectures. As example of applications, somespecial cases are explored, yielding rapidly converging series representationsfor the Ap\'{e}ry constant, $\zeta(3)$, and the Catalan constant, $G =\beta(2)$. Interestingly, our series for $\,\zeta(3)\,$ converges faster thanthat used by Ap\'{e}ry in his irrationality proof (1978). Also, our series for$\,G\,$ converges faster than a celebrated one discovered by Ramanujan (1915).At last, I present a simpler, more direct proof for a recent theorem byKatsurada which generalizes the above results.

A simpler proof of a Katsurada's theorem and rapidly converging series for $\zeta{(2n+1)}$ and $\beta{(2n)}$