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Calculus IV
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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:

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)

Download/Print Prof. Keely's Sequences and Series Formula Sheet (from precalculus)

Supplemental Resources (optional)

Paul's OL Notes - Calc II: Sequences and More on Sequences

Selwyn Hollis's Video Calculus: Sequences 1 and Sequences 2

Patrick JMT Just Math Tutorials:
Factorials – Evaluating Factorials! Basic Info
What is a Sequence? Basic Sequence Info
Geometric Sequences: A Quick Intro
Geometric Sequences: A Formula for the n-th Term
Sequences – Examples Showing Convergence or Divergence
Recursive Sequences

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.