Infinite Limits of Sequences at Infinity

In this video I go over the notation and precise definition for sequences that diverge to infinity when the number of terms go to infinity. The precise definition states that the limit of a sequence approaches infinity if for every positive number M there is a corresponding integer N such that the terms of the sequence are greater than M whenever the n-th term is greater than N. Just as with limits in general, the infinite limit of a function at infinity is the same as that for a sequence except that we are dealing with integer values for the domain of sequences.

#math #limits #sequences #algebra #education

Timestamps:

- Notation for infinite limits: 0:00
- Definition 3: Precise definition for an infinite limit at infinity: 0:36
- Definition for sequences is similar to functions: 1:18
- Graphing infinite limit at infinity for functions: 1:45
- Graphing corresponding infinite limit at infinity for sequences: 3:30
- Infinite limits at infinity are said to be divergent or diverges to infinity: 5:25

Notes and playlists:

- Summary: https://inleo.io/threads/view/mes/re-leothreads-uw4hpwl
- 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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