I thought u could guestimate the amount of the entire harmonic series.......somehow............there may be a way...............from doing something like what Gauss did to get the amount of 1 - 100............by taking the jumps............b/c for every power of ten........the 1........just moves one digit to the right.........

Doing that for the 1st 10 terms.....................does not give u an exact amount..................from 1.10 to 1/100...................u could add 0.1 and 0.01..........................and make pairs out of the fractions......but the problem is that they do not decrease uniformly............so it is an estimate..........

1	1.0000000
1/10	0.1000000
1/100	0.0100000