# Sigma notation

##### Examples

###### Lessons

- Evaluate the following arithmetic series:

- Write the following sum in sigma notation, then evaluate

$7+9+11+13+...+205$

- Evaluate the following geometric series:

- Write the following sum in sigma notation, then evaluate

$-100+10-1+\frac{1}{10}-\frac{1}{100}$ - Use sigma notation to express $S_{10}$ for $-5, 10, -20, 40, ...$, then evaluate

- Evaluate the following infinite geometric series:

- Write the following sum in sigma notation, then evaluate

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###### Topic Notes

Don't you find it tiring when we express a series with many terms using numerous addition and/or subtraction signs? Don't you wish that we have something to symbolise this action? Well we have a solution, introducing the "Sigma Notation"! In this section, we will learn how to utilise the sigma notation to represent a series, as well as how to evaluate it.

$\sum_{i=1}^n$(an equation containing $i$)

$\sum$ : "Sigma"; summation of $i^{th}$ term to $n^{th}$ term

$i$ : index, a counter for the $i^{th}$ term

$n$ : index of ending term

$\sum$ : "Sigma"; summation of $i^{th}$ term to $n^{th}$ term

$i$ : index, a counter for the $i^{th}$ term

$n$ : index of ending term

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