MATH 242: Analysis 1 (McGill Final)

Currently Playing: Proof: Limit Law for Constant Times a Convergent Sequence | 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 🛍 Check out my math clothing store: 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 We prove the limit law for a constant multiplied by a convergent sequence. If a_n converges to a and c is a real number, then the sequence c*a_n converges to c*a. As in, the constant multiple of a convergent sequence converges to its limit multiplied by the same constant. This is a straightforward proof using the epsilon definition of a convergent sequence, except for the case where c is 0. If c = 0, our result follows from the fact that a convergent sequence converges to its constant value. 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