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 (called addends, or sometimes summands) 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 (or even monoid). For finite sequences of such elements, summation always produces a well-defined sum (possibly by virtue of the convention for empty sums).
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Some articles on sum:
... is practical if and only if and, for every i from 2 to k, where denotes the sum of the divisors of x ... this condition is clearly necessary in order to be able to represent as a sum of divisors of n ... condition above, then any can be represented as a sum of divisors of n, by the following sequence of steps Let, and let ...
... To show the second equality, distribute the product over the sum in the result, every product of primes appears exactly once, so by the fundamental theorem of arithmetic, the sum is equal to the ... The sum on the right is the harmonic series, which diverges ...
... A classic example of Jensen's device is a procedure that computes the sum of a series, real procedure Sum(k, l, u, ak) value l, u integer k, l, u real ak comment k and ak ... to compute the first 100 terms of a real array V would be Sum(i, 1, 100, V) ... During the execution of Sum, the actual argument i will increment during each step of the for loop, and each of the procedure's evaluations of ak will ...
... resistant hash function even if the hash sum file is not tampered with, it is computationally trivial for an attacker to cause deliberate hash collisions, meaning that a malicious change in the file is not ...
... In statistics, the residual sum of squares (RSS) is the sum of squares of residuals ... It is also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE) ... In general, total sum of squares = explained sum of squares + residual sum of squares ...
More definitions of "sum":
- (noun): The final aggregate.
Example: "The sum of all our troubles did not equal the misery they suffered"
Synonyms: summation, sum total
- (noun): A quantity of money.
Example: "He borrowed a large sum"
Synonyms: sum of money, amount, amount of money
- (noun): The basic unit of money in Uzbekistan.
- (noun): The choicest or most essential or most vital part of some idea or experience.
Synonyms: kernel, substance, core, center, essence, gist, heart, heart and soul, inwardness, marrow, meat, nub, pith, nitty-gritty
Famous quotes containing the word sum:
“The sum and substance of female education in America, as in England, is training women to consider marriage as the sole object in life, and to pretend that they do not think so.”
—Harriet Martineau (18021876)
“To help, to continually help and share, that is the sum of all knowledge; that is the meaning of art.”
—Eleonora Duse (18591924)
“If the twentieth century is to be better than the nineteenth, it will be because there are among us men who walk in Priestleys footsteps....To all eternity, the sum of truth and right will have been increased by their means; to all eternity, falsehoods and injustice will be the weaker because they have lived.”
—Thomas Henry Huxley (182595)