Theorems · Theorem · sequences and series
summable_descFactorial_mul_geometric_of_norm_lt_one
∀ {R : Type u_4} [inst : NormedRing R] [HasSummableGeomSeries R] (k : ℕ) {r : R},
‖r‖ < 1 → Summable fun n => ↑((n + k).descFactorial k) * r ^ n- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- AddCommMonoidproof · cited by 12,281
- Norm.normstatement and proof · cited by 5,413
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- NormedRingstatement and proof · cited by 924
- Summablestatement and proof · cited by 778
- Nat.factorialproof · cited by 616
- SummationFilterproof · cited by 607
- Nat.chooseproof · cited by 494
- Nat.cast_mulproof · cited by 309
- Nat.descFactorialstatement and proof · cited by 68
Cited by1
Results whose statement or proof uses this declaration.
- summable_pow_mul_geometric_of_norm_lt_oneproof · cited by 1