1. Chapter 9
Infinite Series

2. Definition of the Limit of a Sequence and Figure 9.1
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3. Theorem 9.1 Limit of a Sequence
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4. Theorem 9.2 Properties of Limits of Sequences
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5. Theorem 9.3 Squeeze Theorem for Sequences
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6. Theorem 9.4 Absolute Value Theorem
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7. Definition of a Monotonic Sequence
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8. Definition of a Bounded Sequence
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9. Theorem 9.5 Bounded Monotonic Sequences
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10. Definitions of Convergent and Divergent Series
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11. Theorem 9.6 Convergence of a Geometric Series
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12. Theorem 9.7 Properties of Infinite Series
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13. Theorem 9.8 Limit of nth Term of a Convergent Series
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14. Theorem 9.9 nth-Term Test for Divergence
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15. Theorem 9.10 The Integral Test
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16. Theorem 9.11 Convergence of p-Series
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17. Theorem 9.12 Direct Comparison Test
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18. Theorem 9.13 Limit Comparison Test
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19. Theorem 9.14 Alternating Series Test
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20. Theorem 9.15 Alternating Series Remainder
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21. Theorem 9.16 Absolute Convergence
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22. Definitions of Absolute and Conditional Convergence
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23. Theorem 9.17 Ratio Test
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24. Theorem 9.18 Root Test
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25. Guidelines for Testing a Series for Convergence or Divergence
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26. Summary of Tests for Series
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27. Summary of Tests for Series (cont’d)
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28. Definitions of nth Taylor Polynomial and nth Maclaurin Polynomial
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29. Theorem 9.19 Taylor's Theorem
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30. Definition of Power Series
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31. Theorem 9.20 Convergence of a Power Series
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32. Theorem 9.21 Properties of Functions Defined by Power Series
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33. Operations with Power Series
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34. Theorem 9.22 The Form of a Convergent Power Series
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35. Definitions of Taylor and Maclaurin Series
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36. Theorem 9.23 Convergence of Taylor Series
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37. Guidelines for Finding a Taylor Series
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38. Power Series for Elementary Functions
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