# Sigma notation

### Sigma notation

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.

#### Lessons

$\sum_{i=1}^n$(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
• 1.
Evaluate the following arithmetic series:
a)
$\sum_{i=1}^{10}i$

b)
$\sum_{i=1}^{5}-3(i+1)$

• 2.
Write the following sum in sigma notation, then evaluate
$7+9+11+13+...+205$

• 3.
Evaluate the following geometric series:
a)
$\sum_{i=1}^3 2(\frac{1}{2})^i$

b)
$\sum_{i=1}^{20} (-3)^{i+1}$

• 4.
Write the following sum in sigma notation, then evaluate
$-100+10-1+\frac{1}{10}-\frac{1}{100}$

• 5.
Use sigma notation to express $S_{10}$ for $-5, 10, -20, 40, ...$, then evaluate

• 6.
Evaluate the following infinite geometric series:
a)
$\sum_{i=1}^{\infty} 3(-5)^{i-1}$

b)
$\sum_{i=1}^{\infty} -\frac{7}{2}(-\frac{2}{3})^i$

• 7.
Write the following sum in sigma notation, then evaluate
a)
$4+2+1+...$

b)
$1-2+4-8+...$