1. Sequences
Lesson 8.1

2. Definition A succession of numbers Example
Listed according to a given prescription or rule
Typically written as a1, a2, … an
Often shortened to { an }
Example
1, 3, 5, 7, 9, …
A sequence of odd numbers

3. Finding the nth Term We often give an expression of the general term
That is used to find a specific term
What is the 5th term of the above sequence?

4. Sequence As A Function Define { an } as a function
Domain set of nonnegative integers
Range subset of the real numbers
Values a1, a2, … called terms of the sequence
Nth term an called the general term
Some sequences have limits
Consider

5. Converging Sequences Note Theorem 9.2 on limits of sequences
Limit of the sum = sum of limits, etc.
Finding limit of convergent sequence
Use table of values
Use graph
Use knowledge of rational functions
Use L'Hopital's Rule

6. Divergent Sequences Some sequences oscillate
Others just grow beyond bound

7. Determining Convergence
Manipulate algebraically
Simplify and take the limit
conjugate expressions

8. Determining Convergence
Consider
Use l'Hôpital's rule to take the limit of the function
Note we are relating limit of a sequence from the limit of a continuous function

9. Bounded, Monotonic Sequences
Note difference between
Increasing (decreasing) sequence
Strictly increasing (decreasing) sequence
Note concept of bounded sequence
Above
Below Bounded implies convergent
Both

10. Assignment
Lesson 9.1
Page 602
Exercises 1 – 93 EOO