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: @mes/re-leothreads-gdnl3vjt
• Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUgfK34Voi6BvrNqt4X4BV
• Notes: @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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