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Fix 1994 A1
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The statement should be that the sum diverges, rather than that it has
no finite limit (even though these are easily equivalent given the
latent positivity hypotheses).
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ocfnash committed Oct 23, 2024
1 parent fac23f2 commit 958aaea
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions lean4/src/putnam_1994_a1.lean
Original file line number Diff line number Diff line change
Expand Up @@ -7,7 +7,7 @@ open Filter Topology
Suppose that a sequence $a_1,a_2,a_3,\dots$ satisfies $0<a_n \leq a_{2n}+a_{2n+1}$ for all $n \geq 1$. Prove that the series $\sum_{n=1}^\infty a_n$ diverges.
-/
theorem putnam_1994_a1
(a : ℕ → ℝ)
(ha : ∀ n ≥ 1, 0 < a n ∧ a n ≤ a (2 * n) + a (2 * n + 1))
: ¬(∃ s : ℝ, Tendsto (fun N : ℕ => ∑ n : Set.Icc 1 N, a n) atTop (𝓝 s)) :=
sorry
(a : ℕ → ℝ)
(ha : ∀ n ≥ 1, 0 < a n ∧ a n ≤ a (2 * n) + a (2 * n + 1)) :
Tendsto (fun N : ℕ => ∑ n : Set.Icc 1 N, a n) atTop atTop :=
sorry

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