If I click, then this shows up . . .
If you junk that "1-dim element with finite size X" crap and use "baseline s0 = a" and proceed the way Koch did, then you take the line and cut it in 3 equidistant line segments:
_________|__________|___________
You see that 3 refers to the denominator of the limit of the sum. Then you turn the middle segment by 60 degrees up and add additional line segment to connect the form. Now you see 4 segments the number of which agrees with the numerator of the limit of the sum that you hold wrong. Since the combined length of the segment is greater than the original baseline s0, you need to apply a reduction formula to keep Iteration 0 = Iteration 1. The reduction formula is
Length of the baseline for Iteration N = a*3N/22N
Now the combined length of those 4-line segments of Iteration 1 equals the combined length of the 3-line segment of Iteration 0, which is the "non-bended" line.
Just take into account that your vaguely stated additional conditions can't alter the fact that the limit 4/3 of the above sum is correct.