erdos_317

Is there some constant $c>0$ such that for every $n\geq 1$ there exists some $\delta_k\in \{-1,0,1\}$ for $1\leq k\leq n$ with \[0< \left\lvert \sum_{1\leq k\leq n}\frac{\delta_k}{k}\right\rvert < \frac{c}{2^n}?\]

theorem erdos_317 : answer(sorry) ↔
    ∃ c > 0, ∀ n ≥ 1, ∃ δ : Fin n → ℚ,
      Set.range δ ⊆ {-1, 0, 1} ∧
      letI lhs : ℝ

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