tsum telescope inv
ProvedBlockCycleRotation.tsum_telescope_invanalytic-number-theoryblock-cycle-rotationnumerical-bounds
A supporting lemma of the formalization, declared as tsum_telescope_inv.
This is an auxiliary lemma of the formalization rather than a result stated in the paper.
Preamble
import Mathlib open Real Finset Filter Topology
Formal statement
theorem BlockCycleRotation.tsum_telescope_inv {K : ℕ} (hK : 0 < K) :
∑' j : ℕ, (1 / ((j : ℝ) + (K : ℝ)) - 1 / ((j : ℝ) + (K : ℝ) + 1)) = 1 / (K : ℝ) := by sorrySource
Valentin Blomer and Kai-Uwe Bux, "The cost of cyclic permutations and remainder sums in the Euclidean algorithm", AofA 2026, LIPIcs vol. 381, pp. 14:1-14:17, doi:10.4230/LIPIcs.AofA.2026.14. Numbering follows the full version, arXiv:2601.00979v1. Lean source: https://github.com/dbenbenn/block-cycle-rotation/blob/f69003fd8b00c9b5d6d1a4f6807b4943bce0a92c/BlockCycleRotation/Numeric.lean#L507-L555