MAT 1236 Calculus III Sigma Notations Sage Lab

MAT 1236 Calculus III Sigma Notations + Sage Lab 2 http: //myhome. spu. edu/lauw

HW and… l l Web. Assign HW Download HW, no need to turn in. You are still expected to do it.

Summation Notation l l Index shifting Very useful in • MAT 3727 Differential Equations • MAT 3724 Applied Analysis • Other courses uses series.

Ambiguity

Ambiguity

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

Example 0 Indices are “dummy”

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

Theorem Finite limits

Example 1 (Telescoping Sum) Undesirable Method

Index Shifting l Sigma representation of a summation is not unique

Index Shifting l Sigma representation of a summation is not unique

Index Shifting l Sigma representation of a summation is not unique

Index Shifting l Sigma representation of a summation is not unique

Index Shifting Rules

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

Expectations l

Maple Lab 11. 2 Explore and understand l the convergence of a series l some examples of standard series

Definition l

Example 1 l