Calculus 2     Lesson 11.1     Sequences 
The following topics are the most important. Typical exercises from Calculus, 7th edition-Early Transcendentals, by James Stewart, are assigned at the end of each objective.  

In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective
1. Define sequence, limit of a sequence, convergence of a sequence.   P700#1
P690 The opening paragraphs of this section give the definition of sequence.  Read the section through the notation and memorize the notation.  Look at examples 1 and 2.
  P690 Look at the video in the ebook for Example 2
P692 The definitions of limit of a sequence and convergence of a sequence are given in box 1.  Look at figures 4 and 5.
2. Find the formula for the general term {an}.   P700#13,15
P690 Look at example 1 to try to match the problem to one of these "types".
3. Determine whether a sequence converges or diverges using:
3a. "connect the dots", i.e., limit of f(x) by Chapter 2 methods;   P700#19,35,43
P693 The theorem in box 3 and figure 6 give the sense of this method.
3b. "connect the dots", i.e., limit of f(x) by l'Hopital's rule;   P700#31,41
P694 Example 4 illustrates the use of l'Hospital's Rule in finding the limit of the sequence.
3c. geometric sequence,  {a rn};  P700#22,28
P696 The convergence of geometric sequences rule is given in box 9 on this page.  Example 10 goes through the rationale.
  P695 Look at the video in the ebook for Example 10
  P696 Look at the video in the ebook for Example 11
3d. p-sequence,  {1/np};   P700#26
P693 See Box 4. Use the method in Example 4 or the limit law for ratios.
3e. sandwich theorem;   P700#45
P694 Use the squeeze theorem for sequences.
3f. absolute value to zero theorem;   P700#21
P694 Use the squeeze theorem for sequences to prove the theorem in box 6.
3g. bounded monotonic theorem;   P701#67
P696 The definitions for monotonic (both increasing and decreasing) are found in box 10.  Know the definitions.
P697 The definitions for bounded (both above and below) are found in box 11.  Know the definitions.
P698 The theorem for bounded, monotonic sequences is found in box 12.  Know the result.
3h. graphing calculator for directly or recursively defined sequences.   P700#57-65
P699 Look at the margin note on the page and follow the directions.
4. Determine whether a sequence is monotone increasing or monotone decreasing by either using inequalities or by connecting the dots and using the derivative .   P701#72-78
P695 Look at examples 10 and 11.
5. State and explain the completeness property.   Text
P698 The Completeness Axiom is given in the paragraph below box 11.  Know the result.
For a synopsis of these tests, see Sequence tests

Maple Assignment: See Maple Assignment