lean_workbook_plus_36726

⚠️ 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 an example of real number sequence $\{ a_n \}$ s.t. $\Sigma (a_n^{\ k})$ is converge for any odd natural number $k$ , but $\Sigma |a_n|$ diverge .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_36726 : ∃ (a : ℕ → ℝ), (∀ k : ℕ, Odd k → Summable (λ n : ℕ => (a n)^k)) ∧ ¬ Summable (λ n : ℕ => |a n|)   :=  by sorry

State convergence of the ordered partial sums ∑n=0..N of the series, not Mathlib Summable; the intended conditional convergence for positive odd powers does not imply absolute or unconditional summability.

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

Proposed corrected statement

State convergence of the ordered partial sums ∑n=0..N of the series, not Mathlib Summable; the intended conditional convergence for positive odd powers does not imply absolute or unconditional summability.

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.