Secrets of the Sum of Sums - Paradoxical Harmonic Series

Explore the fascinating world of the harmonic series in this 47-minute video lecture. Delve into the secrets of this prototypical infinite series, uncovering its amazing properties and lesser-known aspects. Begin with a balanced warm-up before tackling the leaning tower of maths. Investigate whether the series is finite or infinite, and examine the concept of terrible aim. Discover how the series gets better and better, and explore the idea of it becoming thinner and thinner. Witness Kempner's proof animation and gain insights into this mathematical marvel. Perfect for mathematics enthusiasts and educators looking to expand their knowledge and teaching repertoire.

Intro.
Chapter 1: Balanced warm-up.
Chapter 2: The leaning tower of maths.
Chapter 3: Finite or infinite.
Chapter 4: Terrible aim.
Chapter 5: It gets better and better.
Chapter 6: Thinner and thinner.
Kempner's proof animation.
Credits.