Hacker News Reader

The harmonic series grows incredibly slowly but has no upper bound.

.00001/1 + .00001/2 + .00001/3 ... => infinity. The ant will eventually pass 100% of the band.

There are lots of counter intuitive results based on the fact the harmonic series has no bound. I remember an article where someone showed you could stack dominoes to produce infinite overhang, exploiting the same counter intuitive bit of math.

View on HN

Perhaps the most interesting and useful fact about the harmonic series is that the nth harmonic number (the partial sum of the first n terms) is an extremely accurately approximation of ln(n) (they are very close for all values of n, in the limit they differ only by the Euler-Mascheroni constant, which is about 0.577). This is the only approximation I have seen that has constant error in the limit.

Reply on news.ycombinator.com