erdos_267.variants.generalisation_ratio_limit_to_infinity

Let $F_1=F_2=1$ and $F_{n+1} = F_n + F_{n-1}$ be the Fibonacci sequence. Let $n_1 < n_2 < \dots$ be an infinite sequence with $\frac {n_k}{k} \to \infty$. Must $\sum_k \frac 1 {F_{n_k}}$ be irrational?

theorem erdos_267.variants.generalisation_ratio_limit_to_infinity : answer(sorry) ↔ ∀ (n : ℕ → ℕ),
    StrictMono n → Filter.Tendsto (fun k => (n (k+1) / k.succ : ℝ)) Filter.atTop Filter.atTop →
    Irrational (∑' k, 1 / (Nat.fib <| n k))

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