## Week 29

Reference: Stewart 10.5, 10.6, 10.7

Keywords: Alternating series, alternating series test, absolute convergence, conditional convergence, ratio test, root test

Learning Objectives: The student will be able to:

• Apply the alternating series test for convergence
• Estimate the error of a partial sum of an alternating series
• Explain what it means to say that a series is "absolutely convergent" or "conditionally convergent"
• Use the ratio and root tests to tell if a series is absolutely convergent
• Choose an effective way to test a series for convergence from the variety of tests learned

29.R Power series

Reference: Stewart 10.8, 10.9, 10.10, 10.12

Keywords: Power series, radius of convergence, interval of convergence, Taylor series, Maclaurin series

Learning Objectives: The student will be able to:

• Find the radius of convergence and interval of convergence of a given power series
• Compute the Taylor series and the Maclaurin series for a given function
• Use power-series methods to approximate definite integrals