A sequence is a function that sequentially connects the items of a sequence with a plus sign. Typical series include positive series, staggered series, power series, Fourier series and so on.

Series theory is a branch of analysis; Together with another branch of calculus, it appears in other branches as basic knowledge and tools. Both of them take limit as the basic tool, and study the object of analysis from discrete and continuous aspects, that is, the dependence between variables-function.

Function:

Series is an important tool to study functions and plays an important role in theory and practical application. This is because: on the one hand, many commonly used non-elementary functions can be expressed by series, and the solutions of differential equations are often expressed by series; On the other hand, functions can be expressed as series, so that functions can be studied by series methods, for example, non-elementary functions can be studied by power series, and approximate calculations can be made.