This analysis uncovers conditions under which summable ideals for specific series match those of the harmonic series, indicating nuanced relationships.
The summable ideal for a harmonic series is described by the O’Malley density of subsets of the real line generated by sequences of reals. Since this approach leads to a special kind of summable ideals, we investigate the relationship between them and we find conditions under which summable ideals for specific series coincide with one for the harmonic series.
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Filipczak et al. (2025) studied this question.
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