A combinatorial proof that e ≤ 3.
Submitted for Summer of Math Exposition 2.
Collaboration with Enumerable: https://www.youtube.com/channel/UCBouaWpdXNk6Oo33rF9b7Ew
Special thanks to: https://mobile.twitter.com/dontthinkmeat
More on the binomial theorem: https://en.wikipedia.org/wiki/Binomial_theorem
#combinatorics #math
Chapters:
0:00 - Intro
1:52 - Part 1: Bounded above by 3
9:48 - Part 2: Monotonically increasing
15:52 - Conclusion
Corrections:
17:02 - There's a typo in extension problem 2. The second equality should be 2^(n-1) (n + 1 choose 2), not choose k
17:07 - Clarification in extension problem 4. The product and summation range over n. The x's form a data set with n elements, and we're taking the arithmetic mean and geometric mean. This is known as the AM–GM inequality.
