The interviewer can ask leading questions if the interviewee gets stuck or doesn't consider certain attributes. Seemingly simple questions that actually have depth are good for an interview because it stimulates discussion and can be carried further for more advanced/competent people. Quizzing someone on "trivia" is a terrible test of competence.
Yeah, it's true that good technical questions are an interactive process. But I'm not too confident that the OP actually saw the complexity in that question, and the many naive responses certainly did not. Also in the context of trying to come up with code on the spot, knowing how that infinite sum is going to converge strikes me as a quite helpful piece of trivia.
... although maybe my gripe only came about from knowing enough to immediately see that there had to be some kind of convergence bound, but not knowing/figuring exactly what it was.
