|With sn=1+1/2+1/3+...+1/n, the harmonic series|
diverges - but so slowely, that a numerical experiment does not show that.
Even if a machine would have been adding terms at a rate of
10-9 seconds and would have started 15 billion years ago,
(about 1017 seconds), the value of the sum would still be about Log(1026)
which is less then 60. |
A similar discrepancy between the mathematical fact and experience can be observed in the Petersburg paradox or with recurrence theorems in thermodynamics.
|© Mathematik.com 2001|