Source labels openChecked July 26, 2026

Convergence of the Flint Hills and Cookson Hills series

The Flint Hills series summing $csc(n)^2 / n^3$ from $n=1$ to $\infty$ converges. (Note that we 0-index the series below.)

Sequences and series AMS 40

Mathematical statement

The Flint Hills series summing $csc(n)^2 / n^3$ from $n=1$ to $\infty$ converges. (Note that we 0-index the series below.)

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

flint_hills_series_converges

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem flint_hills_series_converges :    answer(sorry) ↔      Summable (fun n : ℕ =>        1 / ((((n + 1) : ℝ)^3) * (Real.sin (n + 1)^2))) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Wikipedia: Examples of numerical seriesbackground MathWorld: Flint Hills Seriesbackground Alekseyev, On the Flint Hills seriesbackground