We've learned a LOT of tests for determining whether a series converges or diverges, so the next challenge is determining which test would be best to use for a given series.
Here's a summary of the tests we've learned:
Handout: Summary of Series Tests
Note: The book also has a summary on page 677 (1st edition) or page 701 (3rd edition).
Here's a decision chart to help guide you in choosing which test to apply:
Handout: Decision Chart for Series
Here's a video that can also help:
Video: How to choose a convergence test
Assigned Problems from Textbook
Note: This is a scaled-down set of homework problems as compared to the original assignment sheet.
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1st Edition page 668: 4 (Divergence Test), 5, 6 (Comparison Test), 8 (No, only the Geometric Series test gives the actual value of the series), 43, 44, 47, 57, 61 (hint: This is a telescoping series!) page 680: 33,43, 45, 47 3rd Edition Section 10.8, page 703 3, 5, 6 (Ratio Test), 8 (Geometric Series, r = -3/4), 10 (hint: this is a telescoping series...actually evaluate it and check on Wolfram), 15, 17, 23, 41, 43, 55, |