Definitions for summationsəˈmeɪ ʃən
This page provides all possible meanings and translations of the word summation
summation, summing up, rundown(noun)
a concluding summary (as in presenting a case before a law court)
(physiology) the process whereby multiple stimuli can produce a response (in a muscle or nerve or other part) that one stimulus alone does not produce
sum, summation, sum total(noun)
the final aggregate
"the sum of all our troubles did not equal the misery they suffered"
summation, addition, plus(noun)
the arithmetic operation of summing; calculating the sum of two or more numbers
"the summation of four and three gives seven"; "four plus three equals seven"
: An adding up of a series of items.
the act of summing, or forming a sum, or total amount; also, an aggregate
Origin: [Cf. F. sommation. See Sum, v. t.]
Summation is the operation of adding a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed may be integers, rational numbers, real numbers, or complex numbers. Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group. For finite sequences of such elements, summation always produces a well-defined sum. Summation of an infinite sequence of values is not always possible, and when a value can be given for an infinite summation, this involves more than just the addition operation, namely also the notion of a limit. Such infinite summations are known as series. Another notion involving limits of finite sums is integration. The term summation has a special meaning related to extrapolation in the context of divergent series. The summation of the sequence [1, 2, 4, 2] is an expression whose value is the sum of each of the members of the sequence. In the example, 1 + 2 + 4 + 2 = 9. Since addition is associative the value does not depend on how the additions are grouped, for instance + and 1 + both have the value 9; therefore, parentheses are usually omitted in repeated additions. Addition is also commutative, so permuting the terms of a finite sequence does not change its sum.
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