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

Overview

We use calculus techniques to analyze sequences such as finding the limit of a sequence or determining if a sequence is convergent or divergent. Many real-life patterns, processes, and motions can be written as sequences (such as the swing of a pendulum or bouncing of a ball), then calculus applied.

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: explicit formula (for a the term in a sequence), growth rate (of a sequence), increasing, decreasing, nonincreasing, nondecreasing, monotonic, bounded, convergent, divergent, limit of a sequence, bounded monotonic sequence theorem

Supplemental Resources (optional)

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

Selwyn Hollis's Video Calculus:Sequences 2

Patrick JMT Just Math Tutorials:
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.