The Limit of a Sequence

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.

#maths #science #education #algebra

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

Notes and playlists:

- Summary: https://inleo.io/threads/view/mes/re-leothreads-gdnl3vjt
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUgfK34Voi6BvrNqt4X4BV
- Notes: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more
- Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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