Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
12 Cards in this Set
- Front
- Back
Sequence:
|
- usually means that the collection is ordered so that it has an identified first member, second member, ...
- a function whose domain is the set of positive integers |
|
Converge:
|
approach a limit as the number of terms increases without limit
|
|
Diverge:
|
have no limits as a mathematical series
|
|
Definition of the Limit of a Sequence:
|
|
|
Theorem 9.1: Limit of a Sequence:
|
|
|
Theorem 9.2: Properties of Limits of Sequences:
|
|
|
Theorem 9.3: Squeeze Theorem for Sequences:
|
|
|
Theorem 9.4: Absolute Value Theorem
|
if the absolute value sequence converges to 0, the original signed sequence also converges to 0.
|
|
Definition of Monotonic sequence:
|
each successive term is larger than its predecessor
|
|
Definition of Bounded Sequence:
|
|
|
Theorem 9.5: Bounded Monotonic Sequences:
|
|
|
important properties of real numbers:
|
- they are complete:
meaning... - there are no holes or gaps on teh real number line - completeness axiom for real numbers can be used to conclude that if a sequence has an upper bound, it must have a least upper bound. |