`BookProof.ChapterCoherentTemperature.tsum_choose_two` (h : 0 ≤ nbar) : ∑' n : ℕ, ((n + 2).choose 2 : ℝ) * thermalRatio nbar ^ n = 1 / (1 - thermalRatio nbar) ^ 3

Proved

BookProof.ChapterCoherentTemperature.tsum_choose_two

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentTemperature.

BookProof.ChapterCoherentTemperature.tsum_choose_two (h : 0 ≤ nbar) : ∑' n : ℕ, ((n + 2).choose 2 : ℝ) * thermalRatio nbar ^ n = 1 / (1 - thermalRatio nbar) ^ 3

Formalization note: Lean 4 identifier BookProof.ChapterCoherentTemperature.tsum_choose_two.

Preamble

-- Generated from ChapterCoherentTemperature.lean — theorem BookProof.ChapterCoherentTemperature.tsum_choose_two
import Mathlib
import Definitions.Def_ChapterCoherentTemperature
open BookProof.ChapterCoherentTemperature


noncomputable section




variable {nbar : ℝ}

Formal statement

theorem BookProof.ChapterCoherentTemperature.tsum_choose_two (h : 0 ≤ nbar) :
    ∑' n : ℕ, ((n + 2).choose 2 : ℝ) * thermalRatio nbar ^ n
      = 1 / (1 - thermalRatio nbar) ^ 3 := by sorry

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