The Limit of a Sequence

Math Easy Solutions

description

In this video I go over the limit of a sequence, its notation, as well as plotting it on a number line and graphing it out. A sequence is a list of numbers of definite order whose domain is the set of all real integers. If the numbers in the sequence approach a single number, then it is said to have a limit and is convergent. Otherwise, the sequence has no limit and is divergent. In the next video I will discuss a more precise definition of the limit of a sequence.

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Timestamps:

Limit of a sequence that approaches one: 0:00
Plotting the sequence on a number line: 1:31
Graphing the sequence: 2:53
Domain of a sequence is the set of positive integers: 4:07
The difference between 1 and the sequence approaches zero: 4:56
Notation for the limit of a sequence: 6:03
Definition 1: The limit of a sequence: 7:05
- If limit exists, the sequence converges.
- If limit doesn't exist, the sequence diverges.
Two sequences that have a limit L: 8:02
- The first limit goes above L then decreases while approaching L.
- The second limit oscillates above and below L in decreasing amplitude. 8:46