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Power Series and Interval of Convergence (BC Calculus - Unit 10)

Jean Adams
5.3k Followers
Grade Levels
11th - 12th, Higher Education
Formats Included
  • Zip
Pages
8 + 22 slides
$5.50
$5.50
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Jean Adams
5.3k Followers

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Description

Power Series and Interval of Convergence Lesson:
Your AP Calculus BC students will use the definition of a power series, find the radius and interval of convergence, and determine the endpoint convergence of power series.

What is included in this resource?

⭐ Guided Student Notes

Fully-editable SMART Board® Slides

⭐ Homework/Practice assignment

⭐ Content quiz

⭐ Full solution set

Lesson Objective:

★ Understand the definition of a power series

★ Find the radius and interval of convergence of a power series

★ Determine the endpoint convergence of a power series

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NOTE: This lesson has been updated to reflect the changes in the AP Calculus CED Binder .

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College Board® Topics:

Topic 10.13: Radius and Interval of Convergence of Power Series

College Board® Learning Objectives:

LIM-8.D: Determine the radius of convergence and interval of convergence for a power series. (BC Only)

LIM-8.D.1: A power series is a series of the form ∑(an (x-r)^n)

where n is a non-negative integer {an} is a sequence of real numbers, and r is a real number. (BC Only)

LIM-8.D.2: If a power series converges, it either converges at a single point or has an interval of convergence. (BC Only)

LIM-8.D.3: The ratio test can be used to determine the radius of convergence of a power series. (BC Only)

LIM-8.D.4: The radius of convergence of a power series can be used to identify an open interval on which the series converges, but it is necessary to test both endpoints of the interval to determine the interval of convergence. (BC Only)

LIM-8.D.5: If a powe3r series has a positive radius of convergence, then the power series is the Taylor series of the function to which it converges over the open interval. (BC Only)

LIM-8.D.6: The radius of convergence of a power series obtained by term-by-term differentiation or term-by-term integration is the same as the radius of convergence of the original power series. (BC Only)

The unit includes the following topics:

1. Series and Convergence

2. The Integral Test and p-Series

3. Comparison of Series

4. Alternating Series

5. Ratio and Root Tests

6. Taylor Polynomials and Approximations

7. Lagrange Error Bound and Accuracy

8. Power Series and Interval of Convergence

9. Taylor and Maclaurin Series

10. Representing Functions by Power Series


Click HERE to SAVE 20% by buying all INFINITE SEQUENCES & SERIES products, including cooperative activities, in the UNIT 10 MEGA BUNDLE.

You may also be interested in:

Sequences & Series Essentials

Sequences & Series Assessments

Sequences & Series Homework

AP® is a registered trademark of the College Board® which was not involved in the creation of, and does not endorse this product.

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Total Pages
8 + 22 slides
Answer Key
Included
Teaching Duration
Lifelong tool
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