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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.
Using summation notation, ... for instance an arithmetic series has partial sums = ... who also gave a general form for the remainder of the Maclaurin formula. The ...
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. It is also called Abel's lemma or Abel transformation , named after Niels Henrik Abel who introduced it in 1826.
7.2 Sum of reciprocal of factorials. 7.3 Trigonometry and ... See Faulhaber's formula.
In mathematics, especially the usage of linear algebra in mathematical physics and differential geometry, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving brevity.
1. Internal direct sum: if E and F are abelian subgroups of an abelian group V, notation = means that V is the direct sum of E and F; that is, every element of V can be written in a unique way as the sum of an element of E and an element of F.
In mathematics and statistics, the arithmetic mean (/ ˌ æ r ɪ θ ˈ m ɛ t ɪ k / arr-ith-MET-ik), arithmetic average, or just the mean or average (when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection. [1] The collection is often a set of results from an experiment, an ...
The Minkowski sum of two sets and of real numbers is the set + := {+:,} consisting of all possible arithmetic sums of pairs of numbers, one from each set. The infimum and supremum of the Minkowski sum satisfy, if A ≠ ∅ ≠ B {\displaystyle A\neq \varnothing \neq B} inf ( A + B ) = ( inf A ) + ( inf B ) {\displaystyle \inf(A+B)=(\inf A ...