1. Sequence and Series Dr. Geetha Sivaraman Department of Mathematics
St.Joseph’s College(Autonomous),
Tiruchirappalli
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2. Definition of the Limit of a Sequence
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3. Limit of a Sequence
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4. Properties of Limits of Sequences
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5. Squeeze Theorem for Sequences
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6. 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. Bounded Monotonic Sequences
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10. Problems: 1. Prove that convergence of implies the convergence of
Problems: 1. Prove that convergence of implies the convergence of Check whether the converse is true calculate Discuss the convergence of by assuming
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11. Ans: 1)
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12. Ans 2) ½
Ans 3)
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13. Definitions of Convergent and Divergent Series
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14. Convergence of a Geometric Series Positive term series : A series in which the terms are positive after some stage N.
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15. Properties of Infinite Series The convergence or divergence of a positve term series will not be affected if i).by multiplying a non zero scalar to each term ii). By adding or deleting some finite terms.
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16. The Integral Test
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17. Convergence of p-Series
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18. Limit of nth Term of a Convergent Series
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19. nth-Term Test for Divergence
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20. Direct Comparison Test
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21. Limit Comparison Test
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22. Problems:
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23. Determine the Nature of the following Series
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24. Comparision of Ratios:
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25. D’ Alembert’s Ratio Test
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26. Ratio Test
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27. Raabe’s Test
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28. Exercise:
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29. Answers:
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30. Answers:
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31. Answer
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32. Answer
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33. Test the convergence of the following Series
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34. Answers
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35. Cauchy’s Root Test
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36. Geetha

37. Guidelines for Testing a Series for Convergence or Divergence
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38. Summary of Tests for Series
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39. Summary of Tests for Series (cont’d)
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40. Alternating Series Test
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41. Alternating Series Remainder
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42. Absolute Convergence
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43. Definitions of Absolute and Conditional Convergence
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44. Definitions of nth Taylor Polynomial and nth Maclaurin Polynomial
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45. Taylor's Theorem
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46. Definition of Power Series
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47. Convergence of a Power Series
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48. Properties of Functions Defined by Power Series
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49. Operations with Power Series
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50. The Form of a Convergent Power Series
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51. Definitions of Taylor and Maclaurin Series
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52. Convergence of Taylor Series
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53. Guidelines for Finding a Taylor Series
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54. Power Series for Elementary Functions
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