summands

Summands are the constituents of a sum. In mathematics, a sum is an expression formed by adding together two or more terms, and each element that is added is called a summand (often called an addend in some contexts). For example, in the expression 7 + 3x − 4, there are three summands: 7, 3x, and −4.

Summands can be numbers, variables, or more complex expressions. They may be simple constants, single variables, or entire algebraic expressions. In finite sums the number of summands is finite; in infinite sums, the addition continues indefinitely and is called a series, with the individual terms still referred to as summands.

There is a close but nuanced distinction between summands and terms. In many algebra texts, a term is a component of an expression separated by plus or minus signs, whereas summand specifically emphasizes the element being added. Nevertheless, many authors use the terms interchangeably.

Notation and manipulation: In sigma notation, a finite sum is written as the sum over i of a_i, where each a_i is a summand. When simplifying an algebraic expression, like terms are summed to produce a single summand; rearranging summands in a finite sum does not change its value due to commutativity.

In applied contexts, recognizing summands helps in arithmetic calculations, polynomial manipulation, and the study of series. See also addend, term, series, and arithmetic.

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