Theorems · Theorem · sequences and series
geom_series_eq_inverse
∀ {R : Type u_4} [inst : NormedRing R] [HasSummableGeomSeries R] (x : R),
‖x‖ < 1 → ∑' (i : ℕ), x ^ i = Ring.inverse (1 - x)- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- SummationFilter.unconditionalstatement · cited by 2,068
- Units.valproof · cited by 1,966
- tsumstatement · cited by 1,148
- NormedRingstatement and proof · cited by 924
- Ring.inversestatement and proof · cited by 160
- HasSummableGeomSeriesstatement and proof · cited by 60
- Ring.inverse_unitproof · cited by 24
- Units.oneSubproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- hasSum_geom_series_inverseproof · cited by 2