3 ms·
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 b
by jcampbell1 13y ago
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.
- rafekett 13y agoPerhaps 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.