Theorems · Theorem · sequences and series
summable_choose_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).choose k) * r ^ n- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- NormedRingstatement and proof · cited by 924
- Summablestatement · cited by 778
- Nat.choosestatement · cited by 494
- HasSum.summableproof · cited by 98
- HasSummableGeomSeriesstatement and proof · cited by 60
- hasSum_choose_mul_geometric_of_norm_lt_one'proof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- summable_descFactorial_mul_geometric_of_norm_lt_oneproof · cited by 1