Harmonic series and ????-series (video) | Khan Academy

Video transcript- [Instructor] For many hundreds of years, mathematicians have been fascinated by the infinite sum, whichwe would call a series, of one plus 1/2 plus 1/3 plus 1/4, and you just keep addingon and on and on forever. And this is interesting on many layers. One, it just feels like something that would be interesting to explore. It's one over one plus oneover two plus one over three, that each of these terms aregetting smaller and smaller. They're approaching zero, but when you add them all together, these infinite number of terms, do you get a finite number or does it diverge, donot get a finite number? This also shows up in music and this actually might have been one of the early motivationsfor studying this series. Where if you have a fundamental note, a fundamental frequency in music, and the point of this videoisn't to teach you too much about music, but if youhave a fundamental note, that might be a pure Aor something like that. I'm just showing youone of its wavelengt...