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Unformatted text preview: Second Midterm Study Guide Approximately fifty percent of the exam will be on the convergence of specific series. Given a series, you’ll need to be able to identify and apply whichever of the following tests is most appropriate for determining its absolute convergence, conditional convergence, or divergence: Geometric Series Test: Theorem 8.8 on p. 509 Test for Divergence: Theorem 8.9 on p. 515 Integral Test: Theorem 8.11 on p. 516 p-series Test: Theorem 8.12 on p. 519 Direct Comparison Test: Theorem 8.13 on p. 521 Limit Comparison Test: Theorem 8.14 on p. 523 Ratio Test: Theorem 8.21 on p. 539 Root Test: Theorem 8.17 on p. 530 Alternating Series Test: Theorem 8.18 on p. 534 You should be familiar with the fact that absolute convergence implies con- vergence (the text calls this the Absolute Convergence Test - in Theorem 8.20 on p. 538 - although I never used that name). The following topics about series will also be covered: Convergence or Divergence of a Series from the Definition:...
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- Spring '08
- Mathematical Series, fifty percent