Monotone Convergence Theorem

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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.

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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
  1. Typal Academy
  2. math
  3. real analysis
  4. monotone convergence
  5. sequence
  6. some3
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Hi Scholars! What are your favorite examples for bounded/unbounded and monotone/non-monotone sequences? And what theorems/topics in introductory real analysis would you like us to cover in our next lesson?

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