Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / 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
Precalculus II / 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

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

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.