Unit 6: Infinite Series**

Prereq Test 6

Intro

• A sum of infinitely many terms may converge to a finite value. This understanding will be further developed by exploring graphs, tables, and symbolic expressions for series that converge and diverge and for Taylor polynomials. It is paramount to understand previous concepts such as improper integrals.

• The most important question related to this unit:

  • How can the sum of infinitely many discrete terms be a finite value or represent a continuous function?

Overview 6

Inquiry Activity 6

Key Terms

Unit 6 Podcast (coming soon)

6.1 Power Series

6.1.1 Convergent and Divergent Infinite Series

6.1.2 Geometric Series

6.1.3 Representing Functions as Power Series

6.2 Taylor Series and Taylor's Theorem

6.2.1 Taylor Series

6.2.2 Lagrange Error Bound

6.3 Convergence Tests

6.3.1 The nth Term Test for Divergence

6.3.2 Integral Test for Convergence

6.3.3 Harmonic Series and p-Series

6.3.4 Comparison Tests for Convergence

6.3.5 Ratio Test for Convergence

6.3.6 Alternating Series Test for Convergence

6.3.7 Alternating Series Error Bound

6.3.8 Absolute or Conditional Convergence

6.3.9 Radius and Interval of Convergence