math

I think it’s correct as is. The “…” is used when enough information is present to complete the series.

For example, if the series really is anything other than the alphabet as it is commonly understood, (thus excluding “x”,) then that would need to be made clear by the person communicating the series.

For example, we can say with confidence that your example, “1, 2, 3…∞” is indeed the set of natural numbers, including “24” if we were to write them all out.

they're all just placeholders for individual numbers

Just normal variables, although used in a kinda “gotcha” way by obfuscating the “number minus itself” trick. There’s a very common teacher’s trick that relies on the same principle. You balance a certain equation and “prove” on the blackboard that 0=1. It’s incumbent on the students, then, to figure out that halfway through your shenanigans, you divided the right half of the equation by “x-x”. This is dividing by zero, which is impossible, and thus explains your farce.

You could argue it's implied that a-z sequence contains x. But I agree that it's a bit ambiguous.

Here's what a better notation would look like:

(1-x)(2-x)(3-x)...(n-x) for x from N

Or

(b0 - x)(b1 -x)(b2-x)...(bn-x)

This way, both Bn and X could be any number and not just natural ones.

Correct. Let a-z be the first 26 prime numbers and x be an unknown real number, for example. It cannot be categorically stated in this case that it simplifies to zero.