Calculus Chapter 11

Ch 11  Sequences


Ch 11.1 Sequences


Geometric Sequences


Limits of a Sequence


Limits of a Sequence: The Squeeze Theorem


Ch 11.2 Series


Limits of Series


Showing a Series Diverges Using Partial Sums


Geometric Series and the Test for Divergence


Geometric Series – Expressing a Decimal as a Rational Number

Telescoping Series Example


Ch 11.3 The Integral Test and Estimates of Sums


Integral Test


The p-Series Test


Remainder Estimate for the Integral Test


Ch 11.4 The Comparison Tests


The Comparison Test


The Limit Comparison Test


Ch 11.5 Alternating Series


The Alternating Series Test


Alternating Series Estimation Theorem


Ch 11.6 Absolute Convergence and the Ratio and Root Tests


Absolutely and Conditionally Convergent Series


The Ratio Test


The Root Test


Ch 11.7 Strategy for Testing Series


Strategy for Testing Series – Series Practice Problems


Ch 11.8 Power Series


Power Series – Finding the Interval of Convergence


Ch 11.9 Representation of Functions as Power Series


Power Series Representation of Functions


Differentiation and Integration Using Power Series


Ch 11.10 Taylor and Maclaurin Series


Taylor and Maclaurin Series


Multiplication and Division of Power Series


The Binomial Series – Example 1


Using Taylor Polynomials to Approximate Functions


Taylor’s Theorem with Remainder


Using Maclaurin/Taylor Series to Approximate a Definite Integral to a Desired Accuracy