I'm looking to clarify the meaning of a question, and would greatly appreciate any feedback.
Given a function $f_n(x)$, I am to construct an infinite set S such the series $\sum_{n=0}^\infty{f_n'(x)}$ diverges $∀ x∈S$.
At first I was inclined to think the question was asking to determine all values of x for which the series $\sum_{n=0}^\infty{f_n'(x)}$ diverged, but I am not 100% confident in this thinking. Any ideas of what this question is asking?
Note: I've purposely left out what the function $f_n(x)$ is defined to be in an attempt to do the actual question by myself, but if someone would feel like it would help in order to understand the question, I'll include it.
You need only find infinitely many points where it diverges. You may choose $S$ to be the set containing the infinitely many points that you find. By the wording, it is not necessary to find all points where it diverges. For example, depending on the functions the set could contain all numbers $1/n$ where $n$ is a positive integer.