MAT 1236 Calculus III Appendix E Sigma Notations + Maple Lab

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Presentation transcript:

MAT 1236 Calculus III Appendix E Sigma Notations + Maple Lab

HW and… No WebAssign HW Download Appendix E HW HW key posted (?) for the last problem in HW

Summation Notation

Ambiguity

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

Example 0 Indices are “dummy”

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

Theorem Finite limits

Common Formulas

Example 1 (Telescoping Sum)

Index Shifting Sigma representation of a summation is not unique

Index Shifting Sigma representation of a summation is not unique

Index Shifting Sigma representation of a summation is not unique

Index Shifting Sigma representation of a summation is not unique

Index Shifting Rules

decrease the index by 1

Index Shifting Rules increase the index by 1

Example

Example 2 Rewrite such that the lower limit is 0

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

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

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

Definition

Example 1