∀ {𝕜 : Type u_1} (E : Type u_2) [inst : Field 𝕜] [inst_1 : Ring E] [inst_2 : Algebra 𝕜 E] [inst_3 : TopologicalSpace E]
  [inst_4 : IsTopologicalRing E] {c : ℕ → 𝕜} [Nontrivial E] (n : ℕ),
  (FormalMultilinearSeries.ofScalars E c n = 0) = (c n = 0)