Intro Infinite Sequences and Series.ppt

Infinite Sequences and Series is a foundational concept in mathematics that explores the behavior of ordered lists of numbers and their summation, particularly when these lists continue indefinitely.

1. PRE-MIDTERM
INFINITE SEQUENCES & SERIES
CALCULUS III
PREPARED BY: T. CARL

2. DEFINITION OF THE LIMIT OF A SEQUENCE

3. LIMIT OF A SEQUENCE

4. PROPERTIES OF LIMITS OF SEQUENCES

5. SQUEEZE THEOREM FOR SEQUENCES

6. ABSOLUTE VALUE THEOREM

7. DEFINITION OF A MONOTONIC SEQUENCE

8. DEFINITION OF A BOUNDED SEQUENCE

9. BOUNDED MONOTONIC SEQUENCES

10. DEFINITIONS OF CONVERGENT AND
DIVERGENT SERIES

11. CONVERGENCE OF A GEOMETRIC SERIES

12. PROPERTIES OF INFINITE SERIES

13. LIMIT OF NTH TERM OF A CONVERGENT SERIES

14. NTH-TERM TEST FOR DIVERGENCE

15. THE INTEGRAL TEST

16. CONVERGENCE OF P-SERIES

17. DIRECT COMPARISON TEST

18. LIMIT COMPARISON TEST

19. ALTERNATING SERIES TEST

20. ALTERNATING SERIES REMAINDER

21. ABSOLUTE CONVERGENCE

22. DEFINITIONS OF ABSOLUTE AND
CONDITIONAL CONVERGENCE

23. RATIO TEST

24. ROOT TEST

25. GUIDELINES FOR TESTING A SERIES FOR
CONVERGENCE OR DIVERGENCE

26. SUMMARY OF TESTS FOR SERIES

27. SUMMARY OF TESTS FOR SERIES (CONT’D)

28. DEFINITIONS OF NTH TAYLOR POLYNOMIAL
AND NTH MACLAURIN POLYNOMIAL

29. TAYLOR'S THEOREM

30. DEFINITION OF POWER SERIES

31. CONVERGENCE OF A POWER SERIES

32. PROPERTIES OF FUNCTIONS DEFINED BY
POWER SERIES

33. OPERATIONS WITH POWER SERIES

34. THE FORM OF A CONVERGENT POWER SERIES

35. DEFINITIONS OF TAYLOR AND MACLAURIN SERIES

36. CONVERGENCE OF TAYLOR SERIES

37. GUIDELINES FOR FINDING A TAYLOR SERIES

38. POWER SERIES FOR ELEMENTARY FUNCTIONS

39. REFERENCE: