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Summation is the operation of adding a sequence of numbers to get a sum or total. It is usually denoted with the letter sigma . A sum of all the integers from 1 to 5 can be written as: Any operation can be performed on . For instance, A partial sum, where the sum is only of part of a series, is also called a finite sum. If a sum is between a number and infinity, it is called a series and is denoted Infinite sums can be divergent, meaning they do not converge (such as or ), or convergent, meaning they equal a specific value (for instance, ).

## Properties

A convergent sum of any series in which is multiplied by a constant is the same as the entire sum multiplied or divided by said constant. If is a constant then Two convergent series added together with the same index are equal to the series sum of the arguments: Some example sums with closed forms are shown below:   If a sum is geometric, or in the form If the sum of a geometric series is infinite and convergent , the formula simplifies to: If , then: 