**About this course: **Calculus Two: Sequences and Series is an introduction to sequences, infinite series, convergence tests, and Taylor series. The course emphasizes not just getting answers, but asking the question "why is this true?"

**About this course: **Calculus Two: Sequences and Series is an introduction to sequences, infinite series, convergence tests, and Taylor series. The course emphasizes not just getting answers, but asking the question "why is this true?"

**Taught by:** Jim Fowler, Professor

Commitment | 13 hours of videos and quizzes |

Language | English, Subtitles: Chinese (Simplified) |

How To Pass | Pass all graded assignments to complete the course. |

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Syllabus

WEEK 1

Sequences

Welcome to the Course

What is a Sequence?

What are Some Examples of Sequences?

What is the Limit of a Sequence?

Why Do We Care?

What Other Properties Might a Sequence Have?

How Big Can Sequences Be?

Review

WEEK 2

Series

Introduction to Series

What is a Series? What is a Geometric Series?

What is a Telescoping Series? How Can I Prove That Some Series Diverge?

What is the Harmonic Series? What About More Complicated Series?

What is Point Nine Repeating? What About Numbers That "Go to the Left" Instead of the Right?

Review

WEEK 3

Convergence Tests

Introduction to Convergence Tests

What is the Ratio Test?

What is the Ratio Test Good For?

What is the Root Test? What is the Integral Test?

What Are p-series? How Large Can the Overhang in a Stack of Blocks Be?

Review

WEEK 4

Alternating Series

Introduction to Alternating Series

What is Absolute Convergence?

What is an Alternating Series?

How is Convergence Affected by the Choice of Initial Index? What is the Limit Comparison Test?

Review

WEEK 5

Power Series

Introduction to Power Series

Where Does a Power Series Converge?

What is the Radius of Convergence? What if I'd Like a Power Series in Terms of (x-c)?

Can I Do Calculus With Power Series?

What is a Formula for the Fibonacci Numbers?

Review

WEEK 6

Taylor Series

Introduction to Taylor Series

What Are Taylor Series?

What is Taylor's Theorem?

What Can I Do With This, in Practice? What Can I Do With This, in Theory?

Review

WEEK 7

Final

Final Examination

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