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


There are several "special series" in that they have unique and interesting properties or patterns. For example, Arithmetic Series are sums where terms have a common difference, so you add a constant to a term to get the next term, eg. 2+5+8+11+14+... Geometric Series are sums where terms have a common divisor, so you multiply each term by a constant to get the next term, eg. 2+6+18+54+162+... So are these


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


Terms you should be able to define: arithmetic series, common difference, geometric series, common ratio, telescoping series, harmonic series

Supplemental Resources (recommended)

Download/Print (if you didn't already in LN 11.1) Prof. Keely's Sequences and Series Formula Sheet which includes formulae for arithmetic and geometric series.

Supplemental Resources (optional)

Paul's OL Notes - Calc II: Special Series

Patrick JMT Just Math Tutorials:
Geometric Series: Expressing a Decimal as a Rational Number
Telescoping Series Example

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.