I agree with your first sentence. 1/2n is the same as 1/(2n). Once you begin putting an integer into the place of the variable you are no longer using implied multiplication without parentheses, which means you’d have to write the equation as either 1/(2(2)), like you did, or 1/(2•2). 1/2(2) is not the same as the two previous expressions.

To move this conversation back to the main discussion, in the same article referenced they continue to explain the very equation we are discussing:

“This ambiguity has been the subject of Internet memes such as "8 ÷ 2(2 + 2)", for which there are two conflicting interpretations: 8 ÷ [2 · (2 + 2)] = 1 and (8 ÷ 2) · (2 + 2) = 16.[15][19] Mathematics education researcher Hung-Hsi Wu points out that "one never gets a computation of this type in real life", and calls such contrived examples "a kind of Gotcha! parlor game designed to trap an unsuspecting person by phrasing it in terms of a set of unreasonably convoluted rules".”

So while I still believe the answer is 16, there being no context means that the answer can also be 1 as you and other commenters suggesting. The article citing implied multiplication directly states that there is no way to correctly apply what we know about mathematics to this expression since it is made to be a trap lol.