Monotone Convergence Theorem
Автор: Howard Heaton
Загружено: 2023-08-18
Просмотров: 707
Описание:
As part of our series for real analysis students, our high school intern, Sarah, explains the monotone convergence theorem and a common way it can be applied it to prove sequences converge.
Join our community for real analysis students: https://typal.academy
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This video was submitted to the Summer of Math Exposition contest #SoME3 created by @3blue1brown .
EDIT: At 15:26, there is a typo. After the third equality the fraction "s_n / 2" should actually be written as "1 / (2 * s_n)". Thank you to the viewer that caught this!
Time Stamps:
00:00- Intro
01:01- Monotone Sequences
02:31- Examples for Intuition
04:08- Bounded Sequences
04:43- MCT Proof
09:45- Outline for Applying MCT
10:53- Geometric Sequence Example
14:22- Recursive Sequence Example
17:50- Series Example
21:02- Outro
All diagrams were created using LaTex (including the animations).
#math #realanalysis #sequences
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