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


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.


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


Terms you should be able to 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.