[tgv]

Does anyone understand what the proof is about? An improved boundary on the mean of geometric series? And why it's only a problem for n=3, k=2, and not for all k=n-1?

[pa7x1]

From a very quick glance at page 6 of https://arxiv.org/pdf/2310.05328.pdf

You can see he is treating the case of k=1,2 with that formula and uses induction to extend it to 1 ≤ 𝑘 ≤ 𝑛 − 2.

For k = n - 1 he uses a different bound defined in equation 2.2. So he bypasses the issue.