1. A series converges to λ if the limit of the sequence of the n-thpartial sum of the series is equal to λ

2. Example (1)

5. Warning

6. The Sum of the series

7. Questions Check, whether the given series is convergent, and if convergent find its sum

9. Find the sum of the Series

10. Questions Check, whether the given series is convergent, and if convergent find its sum

12. Find the sum of the Series

13. Example (2) Telescoping Series

15. Warning

17. Examples of this type of telescoping series A Convergent Telescoping Series

18. Solutions

22. Examples of this type of telescoping series A Divergent Telescoping Series

23. Warning

24. Questions I Check, whether the given series is convergent, and if convergent find its sum

25. Hints

26. Questions II Show that the following series is a telescoping series, and then determine whether it is convergent

31. The Integral Test

32. Example (3)

34. Warning

35. Questions Check, whether the given series is convergent.

36. Algebra of Series Convergence

39. Questions

40. Divergence Test

41. Questions Check, whether the given series is convergent.

42. Convergence Tests

43. Convergence Tests for Series of Positive Terms 1. Comparison Test 2. Limit Comparison Test 3. Ratio Test 4. Root Test

44. The Comparison test

45. Examples

46. Example (1)

47. Solution

49. Definition Order of Magnitude of a Series

50. Question

51. The Limit Comparison test

52. Examples

53. Solution

55. The Ratio test

56. Examples

57. The Root test

58. Examples

59. Definition Alternating Series

60. Alternating Series Convergence Test

61. Example

62. Definition Absolute and Conditional Convergence

63. Example (1)

64. Example (2)

65. The Ratio test for Absolute Convergence

66. Examples: Investigate the absolute convergence of the following series

67. More Examples on the Integral Test

68. Example (1)

69. Example (2)

70. Example (3)