Summation - Revision history

Karl Jones: /* External links */

2016-04-24T21:09:19Z

‎External links

Karl Jones at 11:16, 7 February 2016

2016-02-07T11:16:09Z

Karl Jones: fix

2015-08-18T22:14:38Z

fix

Karl Jones: etc

2015-08-18T22:03:20Z

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New page

In [[mathematics]], '''summation''' (symbol: ∑) is the [[addition]] of a [[sequence]] of [[Number|numbers]; the result is their ''sum'' or ''total''.

If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation.

The numbers to be summed (called addends, or sometimes summands) may be integers, rational numbers, real numbers, or complex numbers.

Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group (or even monoid).

For finite sequences of such elements, summation always produces a well-defined sum.

== Series ==

The summation of an infinite sequence of values is called a series. A value of such a series may often be defined, by means of a limit (although sometimes the value may be infinite, and often no value results at all).

== Integration ==

Another notion involving limits of finite sums is integration. The term summation has a special meaning related to extrapolation in the context of divergent series.

== Expression ==

The summation of the sequence [1, 2, 4, 2] is an expression whose value is the sum of each of the members of the sequence.

In the example, 1 + 2 + 4 + 2 = 9.

Because addition is associative, the sum does not depend on how the additions are grouped, for instance (1 + 2) + (4 + 2) and 1 + ((2 + 4) + 2) both have the value 9; therefore, parentheses are usually omitted in repeated additions.

Addition is also commutative, so permuting the terms of a finite sequence does not change its sum (for infinite summations this property may fail; see Absolute convergence for conditions under which it still holds).

== See also ==

* [[Addition]]
* [[Mathematics]]
* [[Number]]
* [[Sequence]]

== External links ==

* [https://en.wikipedia.org/wiki/Summation Summation] @ Wikipedia

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	* [https://en.wikipedia.org/wiki/Summation Summation] @ Wikipedia		* [https://en.wikipedia.org/wiki/Summation Summation] @ Wikipedia
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	In [[mathematics]], '''summation''' (symbol: ∑) is the [[addition]] of a [[sequence]] of [[Number\|numbers]]; the result is their ''sum'' or ''total''.		In [[mathematics]], '''summation''' (symbol: ∑) is the [[addition]] of a [[sequence]] of [[Number\|numbers]]; the result is their ''sum'' or ''total''.
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		+	== Description ==

	If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation.		If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation.

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−	In [[mathematics]], '''summation''' (symbol: ∑) is the [[addition]] of a [[sequence]] of [[Number\|numbers]; the result is their ''sum'' or ''total''.	+	In [[mathematics]], '''summation''' (symbol: ∑) is the [[addition]] of a [[sequence]] of [[Number\|numbers]]; the result is their ''sum'' or ''total''.

	If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation.		If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation.