In this informal seminar we will give a presentation based on practical examples of some of the several methods that can be used to sum hypergeometric series. These series include several known special functions and almost all combinatorial sums. Questions from the public will be welcomed. The goal of the seminar will ultimately be to set the stage for the preparation of a strategy to attack the problem of finding closed form solutions for the problem of the quantum pendulum (that is, to find closed form solutions for the Fourier coefficients of Mathieu functions), from stationary solutions to this problem in the Wigner formalism that were obtained by the speaker.