∀ {f : ℕ → ℂ} {l : ℂ},
  Filter.Tendsto (fun n => ∑ i ∈ Finset.range n, f i) Filter.atTop (nhds l) →
    Filter.Tendsto (fun z => ∑' (n : ℕ), f n * z ^ n) (Filter.map Complex.ofReal (nhdsWithin 1 (Set.Iio 1))) (nhds l)