Summation

Summation is a mathematical operation that combines numbers or quantities. It is represented by the Greek letter sigma (Σ). The process of adding numbers or quantities together is called summation. The result of a summation operation is called a sum or total.

Definition

In mathematics, summation is the addition of a sequence of any kind of numbers, called addends or summands; the result is their sum or total. If the numbers are added together in any order the result is always the same.

Notation

The summation operation can be indicated in various ways:

• Sigma notation is a common method, where the Greek letter sigma (Σ) is used. The upper limit and lower limit of the sum are specified above and below the sigma symbol.
• Euler's notation uses an upper case "E" (from the German word "Einführung", meaning "introduction").
• Capital Pi notation uses the Greek letter Pi (Π) to indicate product, which is the result of multiplication.

Properties

Summation has several properties that make it easier to work with. These include:

• Commutativity: The order of the addends does not change the sum.
• Associativity: Grouping of addends does not change the sum.
• Distributivity: The sum of a product is the product of the sums.

Applications

Summation is used in various fields such as mathematics, physics, statistics, computer science, and economics. It is used to calculate totals, averages, numerical integration, and to solve differential equations.

See also

• Addition
• Subtraction
• Multiplication
• Division
• Mathematical notation

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