Monotone Convergence Theorem

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 ⸻ 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