29.T Infinite
series II <-(READ ME)
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version)
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