∀ {f : ℕ → ℂ} {l : ℂ},
  Filter.Tendsto (fun n => ∑ i ∈ Finset.range n, f i) Filter.atTop (nhds l) →
    ∀ {s : ℝ}, 0 < s → Filter.Tendsto (fun z => ∑' (n : ℕ), f n * z ^ n) (nhdsWithin 1 (Complex.stolzCone s)) (nhds l)