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Consider the variant ... of the series ... , where ... is a non-negative parameter. For ... , the partial sums ... of ... alternate as ... gets large. However, for values of ... in a certain range, there will be a small interval where the sequence of partial sums fails to alternate. That is, there is an ... such that ... or the reverse, ... . It might be an interesting exercise to understand this visually paradoxical phenomenon (see Details for an outline).

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      EUN,LOM,LRE4,work-cmr-id:262343,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/SmallIntervalsWhereThePartialSumsOfASeriesFailToAlternate/,ilox,learning resource exchange,LRE metadata application profile,LRE

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