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Nov 28, 2021 at 18:29 comment added Dmitry Krachun @username well, here we pair summands with indices $n$ and $n+k$, so these are at bounded distance, which is fine
Nov 27, 2021 at 22:27 comment added username My concern is that reordering the order of summation in a semi-convergent series can lead to anything (to any positive of negative real as you know). Can you say a word about why this particular reordering does not change the sum?
Nov 27, 2021 at 21:50 comment added Fedor Petrov @username by partitioning the terms onto pairs as described
Nov 27, 2021 at 18:32 comment added username How do you bound the rest of the sum, $\sum_{2k+1}^\infty \sin\left(\pi \frac nk\right) \frac{1}{n^\alpha}$?
Nov 27, 2021 at 16:26 history answered Dmitry Krachun CC BY-SA 4.0