An infinite series or simply a series is an infinite sum, represented by an infinite expression of the form
where $${\displaystyle (a_{n})}$$ is any ordered sequence of terms, such as numbers See more

Series are classified not only by whether they converge or diverge, but also by the properties of the terms an (absolute or conditional … See more

There exist many tests that can be used to determine whether particular series converge or diverge.
• n-th term test: If $${\textstyle \lim _{n\to \infty }a_{n}\neq 0}$$, … See more

Development of infinite series
Greek mathematician Archimedes produced the first known summation of an infinite series with a method that is still used in the area of … See more

• A geometric series is one where each successive term is produced by multiplying the previous term by a constant number (called the common ratio in this context). For example: See more

Partial summation takes as input a sequence, (an), and gives as output another sequence, (SN). It is thus a unary operation on sequences. Further, this function is See more

A series of real- or complex-valued functions
converges pointwise on a set E, if the series converges for each x in E as an ordinary series of … See more