Here is my entry for Kate Nowak’s Binomial Theorem video contest, clocking in at 17:35.
1. My primary goal was to make something the target audience would be willing to watch. (“Non-honors-math-taking, charming, fallible, fractions-are-dicey, probably-college-bound-but-mostly-not-future-engineers-scientists-mathematicians American high school juniors.”)
2. My secondary goal was to have a complete explanation, without resorting to hand-waving at a pattern.
3. I included two puzzle spots, intending the teacher (or the intrepid viewer) to pause the video.
4. I put the “what’s the nth term” business as a final puzzle, given it’s a somewhat random question to dedicate a whole lesson to anyway (curse you, dark Albany overlords!)
5. The music is from Musopen, a good source for public domain recordings.