putnam-v1 / putnam-1966-b3

putnam-1966-b3

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1966-b3

What it runs

The Lean statement the swarm must prove — kernel-verified at Gate A. The trailing sorry is the open obligation a proof replaces.

goals/putnam-1966-b3.lean

import Mathlib

open Topology Filter

theorem putnam_1966_b3 (p : ℕ → ℝ)
(hpos : ∀ n : ℕ, p n > 0)
(hconv : ∃ r : ℝ, Tendsto (fun m : ℕ => ∑ n ∈ Finset.Icc 1 m, 1/(p n)) atTop (𝓝 r))
: ∃ r : ℝ, Tendsto (fun m : ℕ => ∑ n ∈ Finset.Icc 1 m, (p n) * n^2/(∑ i ∈ Finset.Icc 1 n, p i)^2) atTop (𝓝 r) := by
  sorry

Runs (0)

No runs recorded for this suite yet — they appear here as the swarm attempts the benchmarks.