Course: Calculus III
Topic: Sequences and Infinite Series
Subtopic: Infinite Series


A series is a sum of terms where the terms have some pattern connecting them. Series can be finite such "the sum of the first five prime numbers" 2+3+5+7+11, or infinite such as "the series of positive odd numbers" 1+3+5+7+... going on forever and ever. There are many reasons one might need to write a series to analyze a problem such as studying a bouncing ball going down then up then down then up but not quite as far and adding the total distance traveled by the ball during its bounces. Really pretty fun stuff when you get into it, but a fair amount of terminology and formulae involved too.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: series, infinite series, summation notation, index of the summation, explicit formula, n-th term, sequence of partial sums, convergent series, divergent series

Supplemental Resources (recommended)

Be sure that you can evaluate a summation electronically (eg. using Wolfram Alpha), not just algebraically. For TI graphing calculators see Keely's Calculator Guide: Sequences and Series.

Supplemental Resources (optional)

Paul's OL Notes - Calc II: Series: The Basics

Selwyn Hollis's Video Calculus: Infinite Series

Patrick JMT Just Math Tutorials:
Summation Notation
What is a Series?
Showing a Series Diverges using Partial Sums

More tutorial videos if you need them are listed at James Sousa's MathIsPower4U - Calc II. Scroll down middle column to "Infinite Series" for related titles.