By means of two hypergeometric summation formulae, we establish two large classes of infinite series identities with harmonic numbers and central binomial coefficients. Up to now, these numerous formulae have hidden behind very few known identities of Apéry-like series for Riemann-zeta function, discovered mainly by Lehmer [14] and Elsner [12] as well as Borwein et al. [4, 5, 7]. All the computation and verification are carried out by an appropriately-devised Mathematica package.