Topic 1 – Sequences

• • Sequences Review (Lecture)
  • The Squeeze Thm, Bounded & Monotonic Sequences

Topic 2 – Arithmetic & Geometric Sequences and Series Review; Convergence

• • Series Review (Lecture)
  • Geometric Series and Convergence – The Main Idea
  • Telescoping Series – Basic Example
  • Telescoping Series – Harder Example
  • nth Term Test for Divergence – The Main Idea
  • Find x-values for a Convergent Series Example

Topic 3 – The Integral Test

• • The Integral Test – The Main Idea
  • The Integral Test – Integration by Parts Example
  • p-Series and Integral Test Examples
  • Finding the p-values for which a Series Converges
  • Remainder of the Integral Test – The Main Idea
  • Remainder of the Integral Test – Ex1
  • Remainder of the Integral Test – Ex2

Topic 4 – Comparison Tests

• • Direct Comparison Test – The Main Idea
  • Direct Comparison Test Example
  • Limit Comparison Test – The Main Idea
  • Limit Comparison Test Ex1
  • Limit Comparison Test Ex2
  • Comparison Tests Example 1
  • Comparison Tests Example 2

Topic 5 – Alternating Series Test

• • Alternating Series Test – The Main Idea
  • The AST Remainder
  • Absolute vs Conditional Convergence
  • More Absolute and Conditional Convergence Examples
  • Alternating p-Series Problem

Topic 6 – Ratio and Root Tests

• • The Ratio Test – The Main Idea
  • The Ratio Test Ex1
  • The Ratio Test Ex2
  • The Ratio Test Ex3
  • The Root Test Ex1
  • The Root Test Ex2
  • Finding the Error of a Partial Sum

Topic 7 – Strategy for Testing Series

• • Tests for Series Flowchart (pdf)
  • Tests for Series Table (pdf)
  • Strategy for Testing Series

Topic 8 – Power Series

• • Power Series – The Main Idea
  • Finding Interval of Convergence (I of C) of  Power Series Ex1
  • Finding I of C of a Power Series Ex2
  • Finding I of C of a Power Series f(x), f'(x), Integral of f(x)

Topic 9 – Representing Functions as Power Series

• • Representing Functions as Power Series – The Main Idea
  • Representing Rational Functions as Geometric Series Examples
  • Natural Log Function as a Power Series
  • Arctan Function as a Power Series
  • Exponential Function as a Power Series
  • Approximating a Definite Integral using Power Series
  • Using Calculus to Manipulate Power Series Problem 1
  • Using Calculus to Manipulate Power Series Problem 2

Topic 10 – Taylor and Maclaurin Series

• • Taylor and Maclaurin Series – The Main Idea
  • Taylor Series of y = e^x centered at c = 1
  • The Taylor Remainder – The Main Idea
  • Binomial Series Example