Theorems · Theorem · sequences and series
geom_series_mul_shift
∀ {R : Type u_4} [inst : NormedRing R] [HasSummableGeomSeries R] (x : R),
‖x‖ < 1 → x * ∑' (i : ℕ), x ^ i = ∑' (i : ℕ), x ^ (i + 1)- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 1 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 and proof · cited by 2,068
- tsumstatement and proof · 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.tsum_mul_leftproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- geom_series_mul_one_addproof · cited by 1