Theorems · Theorem · sequences and series
summable_of_ratio_norm_eventually_le
∀ {α : Type u_4} [inst : SeminormedAddCommGroup α] [CompleteSpace α] {f : ℕ → α} {r : ℝ},
r < 1 → (∀ᶠ (n : ℕ) in Filter.atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖) → Summable f- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Filter.Eventuallystatement and proof · cited by 3,134
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- CompleteSpacestatement and proof · cited by 2,532
- Filter.atTopstatement and proof · cited by 2,405
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- SummationFilter.unconditionalstatement · cited by 2,068
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Summablestatement · cited by 778
Cited by2
Results whose statement or proof uses this declaration.
- summable_of_ratio_test_tendsto_lt_oneproof · cited by 2
- Real.summable_pow_div_factorialproof · cited by 1