Summation is the operation of adding a sequence of numbers to get a sum or total. It is usually denoted with the letter sigma (\sum). A sum of all the numbers from 1 to 5 can be written as:


Any operation can be performed on k . 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. Infinite sums can be divergent, meaning they approach infinity (such as \lim_{n\to\infty}\sum_{k=1}^nk=\infty), or convergent, meaning they equal a specific value (for instance, \lim_{n\to\infty}\sum_{k=1}^n\frac1{k^2}=\frac{\pi^2}{6}).


A sum of any series in which k is multiplied or divided by a constant is the same as the entire sum multiplied or divided by said constant. If c is a constant,

\sum_{k=m}^nc\cdot k=c\cdot\sum_{k=m}^nk

If the sequence is of two numbers added to each other, the answer will be the same as the sums of both terms added together.


Sums where k is raised to a power can be found with the following formulas:


If a sum is geometric, or in the form


the sum is equal to


If the sum of a geometric series is infinite and convergent (|r|<1), the formula still applies, but since


we can use the latter formula.

See also

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