Well, I like the challenge as is, but I also think that the magical whatever * has not much practical use - or I cannot imagine one yet but for the simplest sequences.

Which means it would be far simpler and far better to avoid the "magical" and just...

Agreed, there would be too much room for ambiguity. Although TIMTOWTDI is part of the philosophy (* vs. {...}), I guess we will finally end with YABP (BP=best practice):

The Series Operator ...

• Never use the magical whatever (*).
• Define arithmetic and geometric series with an explicit closure.

But it is late and my visionary powers are dwindling ... ;-)