KnowraMonotone sequenceLinked fromLinked fromThe 8 pages that link to Monotone sequence, each with the reason it gives.All 8Related 3Narrower topic 5Alternating series testRelated: The test requires the magnitudes of successive terms to decrease monotonically.Chebyshev's sum inequalityNarrower topic: The hypothesis that both sequences move in the same direction drives the result.Cauchy condensation testNarrower topic: Nonincreasing terms ensure each dyadic block is comparable to its endpoint term.Monotone convergence theoremNarrower topic: The theorem applies precisely to sequences with this order pattern.Abel's testNarrower topic: The other factor must be monotone, allowing its successive differences to be controlled.Kronecker's lemmaNarrower topic: The lemma relies on positive weights that increase monotonically.Stolz–Cesàro theoremRelated: Monotonicity of the denominator sequence is a common sufficient hypothesis.Abel's inequalityRelated: Monotonicity fixes the signs of successive weight differences in the summation-by-parts formula.