  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 of
zeta series. From this result, I have conjectured closed-form summations for
two families of zeta series. Here in this work, I begin by using a known
formula by Wilton to prove those conjectures. As example of applications, some
special cases are explored, yielding rapidly converging series representations
for the Ap\'{e}ry constant, $\zeta(3)$, and the Catalan constant, $G =
\beta(2)$. Interestingly, our series for $\,\zeta(3)\,$ converges faster than
that 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 by
Katsurada which generalizes the above results.
