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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 ...
Sum (category theory), the generic concept of summation in mathematics. Sum, the result of summation, the addition of a sequence of numbers. 3SUM, a term from computational complexity theory. Band sum, a way of connecting mathematical knots. Connected sum, a way of gluing manifolds.
Miscellaneous. v. t. e. In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity. [1] The study of series is a major part of calculus and its generalization, mathematical analysis.
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One can then define the zeta-regularized sum of 1 + 2 + 3 + 4 + ⋯ to be ζ (−1). From this point, there are a few ways to prove that ζ(−1) = − 1 12. One method, along the lines of Euler's reasoning, [12] uses the relationship between the Riemann zeta function and the Dirichlet eta function η ( s ).
Direct sum. The direct sum is an operation between structures in abstract algebra, a branch of mathematics. It is defined differently, but analogously, for different kinds of structures. As an example, the direct sum of two abelian groups and is another abelian group consisting of the ordered pairs where and .
Middle Riemann sum of x ↦ x3 over [0, 2] using 4 subintervals. For the midpoint rule, the function is approximated by its values at the midpoints of the subintervals. This gives f(a + Δx/2) for the first subinterval, f(a + 3Δx/2) for the next one, and so on until f(b − Δx/2). Summing the resulting areas gives.
Summation by parts. In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums.
