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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.
Euler's sum of powers conjecture § k = 3, relating to cubes that can be written as a sum of three positive cubes; Plato's number, an ancient text possibly discussing the equation 3 3 + 4 3 + 5 3 = 6 3; Taxicab number, the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways
Pierre de Fermat gave a criterion for numbers of the form 8a + 1 and 8a + 3 to be sums of a square plus twice another square, but did not provide a proof. [1] N. Beguelin noticed in 1774 [2] that every positive integer which is neither of the form 8n + 7, nor of the form 4n, is the sum of three squares, but did not provide a satisfactory proof. [3]
The first six triangular numbers. The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula
In computational complexity theory, the 3SUM problem asks if a given set of real numbers contains three elements that sum to zero. A generalized version, k-SUM, asks the same question on k elements, rather than simply 3. 3SUM can be easily solved in () time, and matching (⌈ / ⌉) lower bounds are known in some specialized models of computation (Erickson 1999).
Using the visualization of complex numbers in the complex plane, the addition has the following geometric interpretation: the sum of two complex numbers A and B, interpreted as points of the complex plane, is the point X obtained by building a parallelogram three of whose vertices are O, A and B.
The sum of the reciprocals of the pentatope numbers is 4 / 3 . Sylvester's sequence is an integer sequence in which each member of the sequence is the product of the previous members, plus one. The first few terms of the sequence are 2, 3, 7, 43, 1807 . The sum of the reciprocals of the numbers in Sylvester's sequence is 1.
T(n) is the sum of the first n triangular numbers, with T(0) = 0 (empty sum). A000292: Square pyramidal numbers: 0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ... n(n + 1)(2n + 1) / 6 : The number of stacked spheres in a pyramid with a square base. A000330: Cube numbers n 3: 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, ... n 3 = n × n × n ...