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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.
The sum a + b can be interpreted as a binary operation that combines a and b, in an algebraic sense, or it can be interpreted as the addition of b more units to a. Under the latter interpretation, the parts of a sum a + b play asymmetric roles, and the operation a + b is viewed as applying the unary operation +b to a. [20]
A Riemann sum of over [,] with partition is defined as = = (), where = and [,]. [1] One might produce different Riemann sums depending on ...
Legendre's three-square theorem states which numbers can be expressed as the sum of three squares; Jacobi's four-square theorem gives the number of ways that a number can be represented as the sum of four squares. For the number of representations of a positive integer as a sum of squares of k integers, see Sum of squares function.
The mathematical constant e can be represented in a variety of ways as a real number.Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two integers, but it can be represented as a continued fraction.
Sum, an old name for the Finns in East Slavic languages, derived from the word Suomi, "Finland" Soum (currency) (also spelled "sum"), a unit of currency used in some Turkic-speaking countries of Central Asia; SUM (interbank network), an interbank network in 42 U.S. states; SUM, the ISO 639-3 code for the Sumo language; Cen (surname), sometimes ...
In discrete calculus the indefinite sum operator (also known as the antidifference operator), denoted by or , [1] [2] is the linear operator, inverse of the forward difference operator. It relates to the forward difference operator as the indefinite integral relates to the derivative .
In mathematics, an empty sum, or nullary sum, [1] is a summation where the number of terms is zero. The natural way to extend non-empty sums [ 2 ] is to let the empty sum be the additive identity . Let a 1 {\displaystyle a_{1}} , a 2 {\displaystyle a_{2}} , a 3 {\displaystyle a_{3}} , ... be a sequence of numbers, and let