tsum_geometric_le_of_norm_lt_one

∀ {R : Type u_4} [inst : NormedRing R] (x : R), ‖x‖ < 1 → ‖∑' (n : ℕ), x ^ n‖ ≤ ‖1‖ - 1 + (1 - ‖x‖)⁻¹

Bound for the sum of a geometric series in a normed ring. This formula does not assume that the normed ring satisfies the axiom ‖1‖ = 1.

Defined in: Mathlib.Analysis.SpecificLimits.Normed
Cited by: 1 results in Mathlib
Foundations: Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedRing

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.