Theorems · Theorem · sequences and series
Monotone.tendsto_alternating_series_of_tendsto_zero
∀ {f : ℕ → ℝ},
Monotone f →
Filter.Tendsto f Filter.atTop (nhds 0) →
∃ l, Filter.Tendsto (fun n => ∑ i ∈ Finset.range n, (-1) ^ i * f i) Filter.atTop (nhds l)The alternating series test for monotone sequences.
- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- Monotonestatement and proof · cited by 1,397
- Finset.rangestatement · cited by 1,341
- cauchySeq_tendsto_of_completeproof · cited by 10
- Monotone.cauchySeq_alternating_series_of_tendsto_zeroproof · cited by 1
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