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title: Sigma Notation
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## 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")
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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")

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