StanislavKrym comments on Fibonacci Structure in Harmonic Series Partitions

[StanislavKrym]

Explanation of the phenomenon

Denote and notice that the sum of the first Fibonacci numbers Then calculate as follows. We start by noticing that



Additionally, there is the Binet formula implying that which pinpoints to be almost precisely Of course,

However, and
.

Since but , it isn’t surprising that for ANY large enough we have while Therefore, after having cut off the first numbers in step, we cut off the following numbers via the th step.