## Sum

**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:

... 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 ... The

**sum**on the right is the harmonic series, which diverges ...

**sum**

... as CRC32 is not a collision resistant hash function even if the hash

**sum**file is not tampered with, it is computationally trivial for an attacker to cause deliberate hash ...

... if and only if and, for every i from 2 to k, where denotes the

**sum**of the divisors of x ... In one direction, this condition is clearly necessary in order to be able to represent as a

**sum**of divisors of n ... the factorization of n satisfies the condition above, then any can be represented as a

**sum**of divisors of n, by the following sequence of steps Let, and let ...

... 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 are passed by name begin real s s = 0 for k = l ... 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 use the current value of ...

**Sum**Of Squares

... 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":

- (
*verb*): Determine the sum of.

Synonyms: total, tot, tot up, sum up, summate, tote up, add, add together, tally, add up

- (
*noun*): The final aggregate.

Example:*"The sum of all our troubles did not equal the misery they suffered"*

Synonyms: summation, sum total

- (
*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

- (
*noun*): A quantity of money.

Example:*"He borrowed a large sum"*

Synonyms: sum of money, amount, amount of money

### Famous quotes containing the word sum:

“The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a *sum* of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language.”

—Anton Pavlovich Chekhov (1860–1904)

“I would *sum* up my fear about the future in one word: boring. And that’s my one fear: that everything has happened; nothing exciting or new or interesting is ever going to happen again ... the future is just going to be a vast, conforming suburb of the soul.”

—J.G. (James Graham)

“Society does not consist of individuals but expresses the *sum* of interrelations, the relations within which these individuals stand.”

—Karl Marx (1818–1883)