Theorems · Theorem · sequences and series
mul_neg_geom_series
∀ {R : Type u_4} [inst : NormedRing R] [HasSummableGeomSeries R] (x : R), ‖x‖ < 1 → (1 - x) * ∑' (i : ℕ), x ^ i = 1- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- tsumstatement · cited by 1,148
- NormedRingstatement and proof · cited by 924
- HasSummableGeomSeriesstatement and proof · cited by 60
- summable_geometric_of_norm_lt_oneproof · cited by 13
- Summable.one_sub_mul_tsum_powproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Units.oneSubproof · cited by 9