lean_workbook_plus_13803

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Show that the series $\sum_{n=1}^{\infty} \frac{x^n}{3^n n ^2}$ converges pointwise for $-3 < x < 3$ using the ratio test.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_13803 (x : ℝ) (hx : -3 < x ∧ x < 3) (n : ℕ) : ∃ y, ∑' n : ℕ, (x^n / (3^n * n^2)) = y   :=  by sorry

Source