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
Sequences and Infinite Series Power Series Vectors and Geometry of Space Vector-Valued Functions
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Calculus III
Topic: Sequences and Infinite Series
Subtopic: Sequences

Overview

Sequences are basically lists of numbers that have some pattern. For example {2, 5, 8, 11, 14, ...} is a list of numbers starting at 2 and increasing each time by 3 and is known as an arithmetic sequence. You likely studied sequences (and series) in a Precalculus math course. It may help to review particularly the list of objectives (to be sure that you know all that you should) listed in my College Algebra Lesson Notes CALG #8.1, CALG #8.2, CALG #8.3. Here in Calculus we will quickly re-introduce sequences and series and learn to use calculus to apply and analyze them such finding the limit of a sequence or determining if a sequence is convergent or divergent.

Objectives

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

• 11.1.1 Produce examples of sequences and have an intuitive understanding of their having a limit or not
• 11.1.2 Know the difference between a sequence and a series, and for each both finite and infinite
• 11.1.3 Write the sequence of partial sums of a sequence
• 11.1.4 Apply the formal definition of the limit of a sequence
• 11.1.5 Evaluate the limit of a sequence using the limit laws for sequences
• 11.1.6 Recognize an arithmetic sequence and a geometric sequence and be able to write the explicit formula for the n-th term of that sequence
• 11.1.7 Use the Squeeze Theorem for sequences where appropriate to analyze a sequence
• 11.1.8 Identify sequence as increasing, decreasing, nonincreasing, nondecreasing, monotonic, and/or bounded
• 11.1.9 Use the Bounded Monotonic Sequence Theorem where appropriate to analyze a sequence

Terminology

Define: sequence, series, arithmetic sequence, geometric sequence, sequence of partial sums, explicit formula, recursive formula, recurrence relations, growth rates, increasing, decreasing, nonincreasing, nondecreasing, monotonic, bounded, convergent, divergent, limit of a sequence, bounded monotonic sequence theorem

Supplemental Resources (recommended)