1. MAT 1236 Calculus III Appendix E Sigma Notations + Maple Lab http://myhome.spu.edu/lauw

2. HW and… No WebAssign HW Download Appendix E HW Quiz on Thursday: 11.1 II, App. E, 11.2 I No class tomorrow. Take the time to prepare for the next exam HW key posted (?) for the last problem in HW

3. Summation Notation

4. Ambiguity

6. Review: Sigma Notation (Summation) Final value (upper limit) Initial value (lower limit) Index

7. Example 0 Indices are “dummy”

8. Summation Q: Can you name one place in Calculus II where we use the summation notation?

9. Theorem Finite limits

10. Common Formulas

11. Example 1 (Telescoping Sum)

12. Index Shifting Sigma representation of a summation is not unique

13. Index Shifting Sigma representation of a summation is not unique

14. Index Shifting Sigma representation of a summation is not unique

15. Index Shifting Sigma representation of a summation is not unique

16. Index Shifting Rules

17. decrease the index by 1 increase the i in the summation by 1

18. Index Shifting Rules increase the index by 1 decrease the i in the summation by 1

19. Example

20. Example 2 Rewrite such that the lower limit is 0

21. Example 1 Revisit Using “+…+” is ambiguous. We would like to avoid these kind of notations.

22. Expectations Avoid “+…+” by using summations Break up the summations before canceling.

24. Maple Lab 11.2 Explore and understand the convergence of a series some examples of standard series

25. Definition Given a series We define the partial sum sequence {S n }

26. Example 1 Series Partial Sum Sequence {S n }