ยง11.1: Sequences
Core resources for introductory work with sequences. The emphasis here is on sequence notation, explicit and recursive definitions, evaluating terms, viewing a sequence as a function on the positive integers, graphing sequences as discrete points, determining convergence or divergence, and understanding ideas such as boundedness, monotonicity, and recursive behavior.
Library, Handouts & Tools
| Resource Name | Type | Description | Link |
|---|---|---|---|
| OpenStax Calculus: Sequences | Textbook Notes | Strong core reference for sequence notation, limits of sequences, convergence versus divergence, examples, and the monotone convergence viewpoint. | Read Notes |
| Paul's Notes: Sequences | Study Guide | Clear first pass on what a sequence is, how to compute terms, how to graph a sequence, and how to decide whether a sequence converges or diverges. | Read Notes |
| Paul's Notes: More on Sequences | Follow-Up Notes | Useful for the next layer of sequence ideas: increasing/decreasing behavior, boundedness, monotone sequences, recursive definitions, and common sequence vocabulary. | Read Notes |
| OpenStax Chapter 5 Review Exercises | Practice Set | A solid source of mixed sequence questions on convergence, monotonicity, boundedness, and limit evaluation if you want textbook-style review problems. | Open Exercises |
| Khan Academy: Infinite Sequences and Series | Practice Hub | Useful for the sequence-convergence part of the unit, especially if you want quick skill practice and short videos before the course moves deeper into series. | Open Unit |
| Paul's Notes: Sequences Practice Problems | Extra Practice | Extra problems with answers for evaluating terms, finding limits, and classifying sequence behavior after you review the notes. | Practice |
Video Lectures
| Topic | Source | Description | Link |
|---|---|---|---|
| Video Calculus Series (Sequences) | Houston ACT | The UH Video Calculus index explicitly includes monotonicity, boundedness, convergence of bounded monotone sequences, and recursively defined sequences with fixed points and web plots. | Open Page |
| Convergent and Divergent Sequences | Khan Academy | Short introductory video on what it means for a sequence to converge, how to interpret the limit, and what divergence looks like. | Watch |
| Worked Example: Sequence Convergence / Divergence | Khan Academy | Good follow-up video once the definition is clear; it models how to examine several formulas and decide whether the limit exists. | Watch |
| Calculus 2 Series Unit (Start with the Sequence Lessons) | Khan Academy | A useful landing page if you want the sequence videos and exercises collected in one place before moving later into partial sums and full series topics. | Open Unit |
Focused Practice Path
| Skill | Best Resource | What to Focus On | Link |
|---|---|---|---|
| Read and generate terms | Paul's Notes | Practice moving comfortably between sequence notation and actual terms, and make sure you can evaluate formulas such as $a_n$ quickly and accurately. | Start Here |
| Estimate or compute limits | OpenStax | Treat the sequence as a function of $n$ and use familiar limit ideas to decide whether the terms approach a finite value, blow up, or oscillate. | Study Method |
| Analyze monotone and bounded behavior | Paul's Notes | Work carefully with the vocabulary: increasing versus decreasing, bounded above or below, and how those properties connect to convergence. | Review |
| Understand recursive sequences | Houston ACT | Use the UH videos for recursive definitions, fixed points, and web-plot style reasoning so the long-term behavior of a recursive sequence becomes visual instead of mysterious. | Watch Videos |
| Do mixed review | OpenStax / Khan | After the notes, finish with textbook-style review exercises or short online practice sets so you see several types of sequence questions back to back. | Practice Set |