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Calculus with Analytic Geometry
Calculus of a Single Variable
Multivariable Calculus, Seventh Edition
Ron Larson - The Pennsylvania State University, The Behrend
College
Robert P. Hostetler - The Pennsylvania State University, The Behrend College
Bruce H. Edwards - University of Florida | | |
| | Chapter Summary
Chapter 8: Infinite Series
8.1
- List the terms of a sequence.
- Determine whether a sequence converges or diverges.
- Write a formula for the nth term of a sequence.
- Use properties of monotonic sequences and bounded sequences.
8.2
- Understand the definition of a convergent infinite series.
- Use properties of infinite series.
- Use the nth-Term Test for Divergence of an infinite series.
8.3
- Use the Integral Test to determine whether an infinite series converges or diverges.
- Use properties of p-series and harmonic series.
8.4
- Use the Direct Comparison Test to determine whether a series converges or diverges.
- Use the Limit Comparison Test to determine whether a series converges or diverges.
8.5
- Use the Alternating Series Test to determine whether an infinite series converges.
- Use the Alternate Series Remainder to approximate the sum of an alternating series.
- Classify a convergent series as absolutely or conditionally convergent.
- Rearrange an infinite series to obtain a different sum.
8.6
- Use the Ratio Test to determine whether a series converges or diverges.
- Use the Root Test to determine whether a series converges or diverges.
- Review the tests for convergence and divergence of an infinite series.
8.7
- Find polynomial approximations of elementary functions and compare them with the elementary function.
- Find Taylor and Maclaurin polynomial approximations of elementary functions.
- Use the remainder of a Taylor polynomial.
8.8
- 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.
- Differentiate and integrate a power series.
8.9
- Find a geometric power series that represents a function.
- Construct a power series using series operations.
8.10
- Find a Taylor or Maclaurin series for a function.
- Find a binomial series.
- Use a basic list of Taylor series to find other Taylor series.
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