## 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).

Read more about Sum.

### 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 ...

**sum**

... 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 ...

**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":

- (
*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 (1802–1876)

“To help, to continually help and share, that is the *sum* of all knowledge; that is the meaning of art.”

—Eleonora Duse (1859–1924)

“If the twentieth century is to be better than the nineteenth, it will be because there are among us men who walk in Priestley’s 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 (1825–95)