The Precise Definition of a Limit of a Sequence

In this video I go over a more precise definition of the limit of a sequence by using the same approach as for the limit of a function. If the limit of a sequence exists, then there must be a positive number ε such that it has a corresponding number N where if the sequence term n is greater than N, then the absolute value of the difference between the n-th term of the sequence and the limit L is less than ε. Basically this means that even if we approach an infinite number of terms, the number ε just defines a smaller and smaller interval by which the difference between the terms of the sequence and the limit must be within. I also show that the precise definition of the limit of a function is the same as that for the sequence if the limit of the function applies for positive integers. I illustrate this with an example as well.

#maths #science #sequences #algebra #education

Timestamps

• Definition 2: Precise definition of the limit of a sequence: 0:00
• Plotting the definition on a number line: 1:47
• Graphing the precise definition: 5:32
• Recap on the precise definition of a the limit of a function: 9:02
  • N is any real number for functions, and only integers for sequences.
• Theorem 1: Limit of a function is the same as the limit of sequence if n can be an integer: 9:54
• Graphing out Theorem 1 shows the sequence on the function: 10:56
• Example: Limit of a function is zero, thus its corresponding sequence also approaches zero: 12:18

Notes and playlists

• Summary: @mes/re-leothreads-2ly9qbk9k
• 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 .

Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

MES Links: https://mes.fm/links

MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: @mes

Email me: contact@mes.fm

Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

▶️ 3Speak