File:Sigma_summation_notation.svg · Wikimedia Commons · See Wikimedia Commons
Also known as summation, sum of a sequence, total, sigma notation, sumif
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
A sum is the result you get when you add a sequence of numbers together. While summation typically involves numbers, the same addition process can be applied to many other mathematical objects like functions, vectors, and matrices, making it a fundamental operation across different areas of mathematics.
AI-generated from the Wikipedia summary — may contain errors.
~16 min read
Encyclopedic overview
24 sectionsContents
- Notation
- Capital-sigma notation
- Special cases
- Algebraic sum
- History
- Formal definition
- Measure theory notation
- Calculus of finite differences
- Approximation by definite integrals
- Identities
- General identities
- Powers and logarithm of arithmetic progressions
- Summation index in exponents
- Binomial coefficients and factorials
- Involving the binomial theorem
- Involving permutation numbers
- Others
- Harmonic numbers
- Growth rates
- See also
- Notes
- References
- Bibliography
- External links
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
Summations of infinite sequences are called series. They involve the concept of limit, and are not considered in this article.
Excerpted from Wikipedia’s “sum” article, available under the CC BY-SA 4.0 licence.