We explore a counter-intuitive property of proof by induction, where one inequality can be proven by induction easily, but a seemingly easier to prove, weaker, inequality cannot.
Further reading with another pair of examples:
Boyd A.V. An example on mathematical induction. The Mathematical Gazette. 1961;45(353):248-249. doi:10.2307/3612801
00:00 Intro
01:23 Induction works
03:29 Induction doesn't work
06:00 Explanation