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Copyright 2026 The Formal Conjectures Authors.
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import FormalConjecturesUtilConvergence of the Flint Hills and Cookson Hills series
namespace FlintCooksonHills
The Flint Hills series summing $csc(n)^2 / n^3$ from $n=1$ to $\infty$ converges. (Note that we 0-index the series below.)
@[category research open, AMS 40]
theorem flint_hills_series_converges :
answer(sorry) ↔
Summable (fun n : ℕ =>
1 / ((((n + 1) : ℝ)^3) * (Real.sin (n + 1)^2))) := ⊢ True ↔ Summable fun n => 1 / ((↑n + 1) ^ 3 * Real.sin (↑n + 1) ^ 2)
All goals completed! 🐙
The Cookson Hills series summing $sec(n)^2 / n^3$ from $n=1$ to $\infty$ converges.
@[category research open, AMS 40]
theorem cookson_hills_series_converges :
answer(sorry) ↔
Summable (fun n : ℕ =>
1 / ((((n + 1) : ℝ)^3) * (Real.cos (n + 1)^2))) := ⊢ True ↔ Summable fun n => 1 / ((↑n + 1) ^ 3 * Real.cos (↑n + 1) ^ 2)
All goals completed! 🐙
end FlintCooksonHills