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Alternating series of higher mathematics is one of the important contents for staggered series convergence of the Criterion research, in general only the Leibniz Discrimination Act, and Leibniz Discrimination Act has certain limitations, it can not directly determine staggered series is absolutely convergent or conditional convergence.

The oscillating series are one in higher mathematics important contents, collects the divergence distinction method research regarding the oscillating series, generally only involved Leibniz to distinguish the law, but Leibniz distinguished that the law had certain limitation, it was unable to judge the oscillating series is directly the absolute convergence or the conditionally convergent.