A series whose partial sums do not have a finite limit of a sequence. They may grow without bound or oscillate. Some divergent series belong to the domain of a summation method, such as Cesàro summation.
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A divergent series is an infinite series that does not converge to a finite limit. In mathematical terms, a series is expressed as the sum of its terms, such as: \[ S = a_1 + a_2 + a_3 + \ldots + a_n + \ldots \] Where \( a_n \) represents the individual terms of the series. If the partial sums of this series (i.e.