Order summable

Order summability is a concept in the field of summability theory, which deals with the summation of sequences and series, particularly when the usual methods fail to produce a finite limit. It is a generalization of the notion of convergence for series and sequences. In essence, a sequence is said to be **order summable** if it can be summed in a particular way that accounts for the arrangement of its terms, often by weighting or structuring them.