An infinite series or simply a series is an infinite sum, represented by an infinite expression of the form
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Partial summation takes as input a sequence, (an), and gives as output another sequence, (SN). It is thus a unary operation on … See more

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

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

A series of real- or complex-valued functions
$${\displaystyle \sum _{n=0}^{\infty }f_{n}(x)}$$ See more

Development of infinite series
Greek mathematician Archimedes produced the first known summation of an infinite series with a … See more