Theorems · Theorem · sequences and series
summable_pow_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 * r ^ n- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites54
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- AddCommMonoidproof · cited by 12,281
- Polynomialproof · cited by 5,681
- Norm.normstatement and proof · cited by 5,413
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- Finset.sum_congrproof · cited by 2,323
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- mul_assocproof · cited by 1,667
Cited by1
Results whose statement or proof uses this declaration.
- Real.summable_pow_mul_exp_neg_nat_mulproof · cited by 1