Infinite series and products

Determining wether or not a series converges or not always trivial, therefore itis useful to have convergence tests that can be applied in different situations todetermine convergence. This thesis will mainly encompass some properties of series,convergence tests with applications, and and a little about convergence of productsand how they relate to series. The main result of the thesis being a classification ofwhich real values a specified hypergeometric series converges for, using Gauss’s test.