A series is, informally speaking, the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely. Given an infinite sequence of numbers

## Zeno's Paradox

Say you are working from a location

The terms of the series are often produced according to a certain rule, such as by a formula or by an algorithm. As there are an infinite number of terms, this notion is often called an infinite series. Unlike finite summations, infinite series need tools from mathematical analysis, specifically the notion of limits, to be fully understood and manipulated. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, and finance.

## Definition

For any sequence of rational numbers, real numbers, complex numbers, functions thereof, etc., the associated series is defined as the ordered formal sum:

The sequence of partial sums

By definition, the series