lean_workbook_plus_44322

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Find the sum of: $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}k^{2}}{k^{3}+1}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_44322 : ∀ x : ℝ, ∑' k : ℕ, (-1 : ℝ)^(k+1) * k^2 / (k^3 + 1) = x   :=  by sorry

The series is conditionally convergent, so a Mathlib unconditional tsum also does not encode the ordinary ordered sum. No exact value is inferred here.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Restore the task of evaluating the ordered partial-sum limit of the alternating series; remove the universal claim that one fixed sum equals every real x.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.