freeCodeCamp/guide/english/mathematics/sigma-notation/index.md

---
title: Sigma Notation
---
## Sigma Notation

Sigma Notation is a mathematical shorthand for representing large sums.

Sigma Notation is as follows

![alt text](https://github.com/TheRealSpartacus/sources/blob/master/SiGma.PNG "Sigma Notation")
<!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds  -->
where *n* is the lower limit *k* is the upper limit and *a<sub>n</sub>* is the function you are summating

To evaluate a sum in Sigma notation, you first plug in all integers from the *n* to *k* to *a<sub>n</sub>*, then add up all the results.

For example :

![alt text](https://github.com/TheRealSpartacus/sources/blob/master/Sigma%20Fig%201.PNG "Fig. 1")

First, you plug all integers from *n* to *k* into *a<sub>n</sub>* :

![alt text](https://github.com/TheRealSpartacus/sources/blob/master/Sigma%20Fig%202.PNG "Fig. 2")

Second, you evaluate all instances of *a<sub>n</sub>* :

![alt text](https://github.com/TheRealSpartacus/sources/blob/master/Sigma%20Fig%203.PNG "Fig. 3")

Last, you add all the results up, leaving you with the value of the sigma :

![alt text](https://github.com/TheRealSpartacus/sources/blob/master/Sigma%20Fig%204.PNG "Fig. 4")

#### More Information:
<!-- Please add any articles you think might be helpful to read before writing the article -->

<a href="http://www.youtube.com/watch?feature=player_embedded&v=5jwXThH6fg4
" target="_blank"><img src="http://img.youtube.com/vi/5jwXThH6fg4/0.jpg" 
alt="IMAGE ALT TEXT HERE" width="240" height="180" border="10" /></a>