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The summation of an explicit sequence is denoted as a succession of additions. For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands ...
In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through repeated application. [1] Common examples include the extension of the addition operation to the summation operation, and the extension of the multiplication operation to the product operation.
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.
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
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; Digit sum, in number theory; Direct sum, a combination of ...
Five and ten: Sums of the form 5 + x and 10 + x are usually memorized early and can be used for deriving other facts. For example, 6 + 7 = 13 can be derived from 5 + 7 = 12 by adding one more. [36] Making ten: An advanced strategy uses 10 as an intermediate for sums involving 8 or 9; for example, 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14. [36]
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In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value () of some function. An important class of pointwise concepts are the pointwise operations, that is, operations defined on functions by applying the operations to function values separately for each point in the domain of definition.