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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 of the reciprocals of the Proth primes, of which there may be finitely many or infinitely many, is known to be finite, approximately 0.747392479. [2] The prime quadruplets are pairs of twin primes with only one odd number between them. The sum of the reciprocals of the numbers in prime quadruplets is approximately 0.8706.
The nth partial sum is given by a simple formula: = = (+). This equation was known to the Pythagoreans as early as the sixth century BCE. [5] Numbers of this form are called triangular numbers, because they can be arranged as an equilateral triangle.
Columnar addition – the numbers in the column are to be added, with the sum written below the underlined number. There are also situations where addition is "understood", even though no symbol appears: A whole number followed immediately by a fraction indicates the sum of the two, called a mixed number. [4]
In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.)
In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
Computation of the sum 2 + 5 + 8 + 11 + 14. When the sequence is reversed and added to itself term by term, the resulting sequence has a single repeated value in it, equal to the sum of the first and last numbers (2 + 14 = 16). Thus 16 × 5 = 80 is twice the sum.
In mathematics, the digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number 9045 {\displaystyle 9045} would be 9 + 0 + 4 + 5 = 18. {\displaystyle 9+0+4+5=18.}