## 11.4 Outline

- Finite series
- define series
- definition
- alternating series

- Summation notation
- definition
- sigma notation
- evaluate a summation
- expand a summation

- Arithmetic series
- definition
- formula

- Geometric series
- definition
- formula

- Infinite geometric series
- definition
- partial sums
- formula

- Summary of sequence and series formulas

## 11.4 Essential Ideas

If the terms of sequence are added, the expression is called a **series**.

The indicated sum of the terms of a finite sequence *s*_{1}, *s*_{2, }*s*_{3, }…, *s*_{n }is called a **finite series **and is denoted by *S _{n }*=

*s*

_{1}

*+ s*

_{2}

*+s*

_{3}

*+*…

*+s*

_{n}.

An **arithmetic series** is the sum of the terms of an arithmetic sequence.

A **geometric series** is the sum of the terms of a geometric sequence.

If *g*_{1}, *g*_{2, }*g*_{3, }…, *g* _{n}, … is an infinite geometric sequence with a common ratio *r* such that |*r| < *1, then the sum is denoted by *G* and is found by *G = g*_{1}*/*(1 – *r*). If |*r|* is greater than or equal to 1, then the infinite geometric series has no sum.