The question: Find suitable coefficients $(a_n)$ so that $\sum a_n x^n$ has the given properties or Explain why such request is impossible.
Question (a): Converges on every $x \in \mathbb{R}$
Question (b): Diverges on every $x \in \mathbb{R}$
The below are the (potential) answers I want to be checked and/or corrected:
** The space is strictly limited to the Euclidean one
** For (a), it's "which converges for all $x \in \mathbb{R}$"