The Harmonic Sequence Paradox

With s_n=1+1/2+1/3+...+1/n, the harmonic series

lim_n s_n=

1/2

1/3

1/4

1/5

1/6

1/7

1/8

1/9

1/10

1/11

1/12

1/13

1/14

1/15

1/16

...

1/2

1/4

1/8

1/16

...

1/2

...

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.

n	s_n