Theorems · Theorem · sequences and series
Monotone.cauchySeq_alternating_series_of_tendsto_zero
∀ {f : ℕ → ℝ},
Monotone f → Filter.Tendsto f Filter.atTop (nhds 0) → CauchySeq fun n => ∑ i ∈ Finset.range n, (-1) ^ i * f iThe alternating series test for monotone sequences.
See also Monotone.tendsto_alternating_series_of_tendsto_zero.
- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 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 and proof · cited by 25,697
- nhdsstatement and proof · cited by 5,554
- Finset.sumstatement · cited by 5,195
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Finset.sum_congrproof · cited by 2,323
- mul_commproof · cited by 2,262
- Monotonestatement and proof · cited by 1,397
- Finset.rangestatement and proof · cited by 1,341
- CauchySeqstatement and proof · cited by 131
- norm_sum_neg_one_pow_leproof · cited by 2
- Monotone.cauchySeq_series_mul_of_tendsto_zero_of_boundedproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Monotone.tendsto_alternating_series_of_tendsto_zeroproof · cited by 0