MATH 242: Analysis 1 (McGill Final)

Currently Playing: Using the Monotone Convergence Theorem! | Real Analysis

Support the production of this course by joining Wrath of Math to access all my real analysis videos plus the lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Get the coolest math clothes in the world! https://mathshion.com/ Real Analysis course: https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Real Analysis exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC Get the textbook! https://amzn.to/3CMdgjI Let's see an awesome example of the monotone convergence theorem in action! We'll look at a sequence that seems to converge, as its terms change by smaller and smaller amounts, but it isn't clear what it converges to. Since we don't have a clue how we might express its limit, we cannot use our typical method of just proving it converges using the definition of the limit of a sequence. Instead, we'll prove it is monotone increasing and bounded, and thus converges by the monotone convergence theorem! This example is taken from Real Analysis by Jay Cummings. Highly recommended textbook! Bounded Sequences: https://youtu.be/hkCKQdAFLAw Proof of the Monotone Convergence Theorem: https://youtu.be/4NURDmE79VU Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu