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Oct 2 at 19:35 comment added Jorge Zuniga @Steven_Clark Eqs.(5-6) correspond to closed forms of Euler Method to accelerate alternating series applied to these particular cases. Eqs (1-2) on the other side I think they correspond to Abel's summation by parts formula using Newton series. See en.wikipedia.org/wiki/Summation_by_parts
Dec 1, 2023 at 16:44 history edited Steven Clark CC BY-SA 4.0
Added note on convergence of formulas at non-positive integers.
Nov 30, 2023 at 16:20 history asked Steven Clark CC BY-SA 4.0