Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis

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

Overview

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

Objectives

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

• 11.3.1 Recognize arithmetic series, geometric series, telescoping series, harmonic series, and other special series
• 11.3.2 Work with formulae associated with arithmetic sequences and series and formula associated with geometric sequences and series (eg. n-th term, sum of the first n-terms)
• 11.3.3 Determine if arithmetic or geometric series is convergent or divergent and if convergent find to what value
• 11.3.4 Evaluate a telescoping series by expanding and recognizing patterns

Terminology

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.