ABSTRACT In 2002 and 2006, using a Wilf–Zeilberger-based method, Guillera introduced proofs for evaluations for what are considered as the simplest two series out of Ramanujan's 17 series for . In this article, we show how the WZ method may be used in a fundamentally and nontrivially different way to prove these results, and to obtain identities for infinite families of Ramanujan-like series for . We introduce a -recurrence that we had discovered experimentally, and we prove this recursion using the WZ method and apply it to obtain a series acceleration formula that we apply to formulate a new and simple proof for the Ramanujan series for that has a convergence rate of , and we provide an infinite family of generalizations of this formula, and similarly for Ramanujan's series of convergence rate .