## What Does infinite series Mean

A series is a succession of elements that, ordered, maintain a certain link with each other. The notion of infinity , for its part, is linked to that which lacks an end .

An infinite series , therefore, is a series of units that has no end . The opposite concept is that of finite series , which is characterized by ending at a certain moment.

We can understand the notion of infinite series if we think of certain number series . Let's take the case of the number series made up of multiples of 2 . This series is an infinite series since the multiples of 2 are infinite: 0, 2, 4, 6, 8, 10, 12 ...

Series can be understood as sets . The numerical series of positive odd numbers less than 10 , in this sense, is the set that includes the numbers 1, 3, 5, 7 and 9 . As you can see, it is a finite series. On the other hand, if we want to refer to the series of odd numbers , it will be an infinite series : a set with infinite components.

Since the numbers are infinite, we can list all kinds of infinite number series. It is even possible to consider infinite descending series: for example, if we mention the series composed of numbers less than 1 : 0, -1, -2, -3, -4, -5, -6 ...

In addition to all the above, we cannot ignore the fact that there are many and diverse types of infinite series that exist. However, among the most significant we can highlight, for example, the following:

-Harmonic series.

-Geometric series. Under this name there is, for example, a series of infinite type that is characterized by the fact that each term is obtained from what is the multiplication of the previous term by a certain constant.

-Convergent series. When it comes to determining whether an infinite series is convergent or not, various tools can be used. Specifically, among the most common are the p-series, which are summations of functions; the geometric series theorem, the direct comparison criterion, the comparison criterion by passing the limit of the quotient, the Cauchy integral criterion, the d'Alembert criterion and the Leibniz criterion, among many others.

The usual thing is that, in the field of mathematics , infinite series arise from different algorithms, formulas or rules. In this way, infinite series can be used to represent functions .

One of the most important figures in the field of infinite series was and is the Swiss mathematician and physicist Leonhard Euler (1707 - 1783), who is considered the most important mathematician of the 18th century. In the case at hand, it is necessary to underline the fact that he chose to undertake an exhaustive investigation into the development of calculus and that was what led him to establish the mathematical constant as e, which he proceeded to represent not only as a fraction continuous but also as a real number or an infinite series.