Theorems · Theorem · sequences and series
geom_series_mul_one_add
∀ {R : Type u_4} [inst : NormedRing R] [HasSummableGeomSeries R] (x : R),
‖x‖ < 1 → (1 + x) * ∑' (i : ℕ), x ^ i = 2 * ∑' (i : ℕ), x ^ i - 1- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- one_mulproof · cited by 2,841
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- NormedRingstatement and proof · cited by 924
- add_mulproof · cited by 363
- two_mulproof · cited by 232
- add_sub_assocproof · cited by 72
- HasSummableGeomSeriesstatement and proof · cited by 60
- geom_series_succproof · cited by 2
- geom_series_mul_shiftproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- pi_mul_cot_pi_q_expproof · cited by 1