Did I make a "forced" interpretation?

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Just a few years ago I wrote an article called The Geometry of the MRB constant. Since then I've wondered if there is a better, more natural geometric analysis of the following summation. $$ \sum_{k=1}^\infty (-1)^k(k^{1/k}-1) $$

Here is a rough description of what I did: part1

part2

part3