We establish several interesting series associated with the ratio and the product of central binomial coefficients, namely and . Series involving the product of central binomial coefficients can be found in the papers of Campbell, D'Aurizio, and Sondow. In this paper, through the application of integration methods, we address broad generalizations of both classes. The techniques involved in constructing the integrals for the corresponding series are based on the use of the ordinary generating functions of central binomial coefficients and Wallis' well-known integral formulas.