How to characterize the speed of a divergent series ? I have a divergent series with a parameter $x$ in it. How can i characterize the speed of divergence for different $x$ ?
what is the speed of a divergent series?
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sequences-and-series
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0While there are various rates of convergence, based on big-O, little-o, etc. notations, it will not make equal sense to talk about "speed of divergence". A divergent series need not grow uniformly. It might oscillate. Or there might be subsequences that grow and subsequences that oscillate in bounded fashion. One way to impose some consistency on the behavior of nonconvergent sequences is to look at its lim sup and lim inf. Perhaps you should explain the purpose of the characterization you seek. – 2011-01-13
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0@hardmath : the series is non-decreasing – 2011-01-13
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0This is a very vague question. Why don't you show us what series you have... – 2011-01-13
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0@Moron : I don't really have any series to work with, the only restriction is that it is non decreasing. – 2011-01-13