Mariusz, great answer (+1)!
This reminds me of "Ramanujan summation" - is it this you have in mind with your approach?
Because "regular" Regularization options for Sum (e.g. "Euler", "Borel", etc.) do not give a closed solution here.
On the other hand by just omitting diverging terms one could argue like so:
summ = Sum[1/(1 - 2^(-s + 1)), {s, 2, \[FormalM]}];
(* series expansion about m=2, because 2 is the lowest index: *)
Series[summ, {\[FormalM], 2, 0}] // Normal // FullSimplify
(* Out: 2 *)
Where am I wrong? Am I wrong? Regards -- Henrik
