Calculus Two: Sequences and Series

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?"

Week 1: Sequences (19 Apr 2014)

• 1.00 How can I succeed in this course?
• 1.01 What is a sequence?
• 1.02 How is a sequence presented?
• 1.03 Can the same sequence be presented in different ways?
• 1.04 How can we build new sequences from old sequences?
• 1.05 What is an arithmetic progression?
• 1.06 What is a geometric progression?
• 1.07 What is the limit of a sequence?
• 1.08 Visually, what is the limit of a sequence?
• 1.09 Is it easy to find the limit of a sequence?
• 1.10 For some $\mathrm{ϵ<!--\; ϵ\; -->}$, how large need $N$ be?
• 1.11 How do sequences help with $\sqrt{2}$?
• 1.12 When is a sequence bounded?
• 1.13 When is a sequence increasing?
• 1.14 What is the Monotone Convergence Theorem?
• 1.15 How can the Monotone Convergence Theorem help?
• 1.16 Is there a sequence that includes every integer?
• 1.17 Is there a sequence that includes every real number?

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