Series (mathematics)

related topics
{math, number, function}
{theory, work, human}
{film, series, show}
{land, century, early}
{mi², represent, 1st}
{math, energy, light}
{work, book, publish}

A series is 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. [1]

In mathematics, given an infinite sequence of numbers { an }, a series is informally the result of adding all those terms together: a1 + a2 + a3 + · · ·. These can be written more compactly using the summation symbol ∑. An example is the famous series from Zeno's dichotomy

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 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 and computer science.

Contents

Full article ▸

related documents
Newton's method
Integration by parts
Functor
Direct sum of modules
Boolean satisfiability problem
Riemann zeta function
Stone–Čech compactification
List of trigonometric identities
Principal components analysis
Johnston diagram
Russell's paradox
Infinity
Pascal's triangle
Forcing (mathematics)
Complete lattice
Cauchy sequence
Denotational semantics
Ruby (programming language)
Groupoid
Bra-ket notation
Non-standard analysis
Numerical analysis
Mathematical induction
Kernel (algebra)
Cardinal number
Sequence alignment
Gaussian elimination
Entropy (information theory)
Logic programming
Huffman coding