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Infinite series and the derived set of the aggregate of the fractional parts of its partial sums: Addendum
Published online by Cambridge University Press: 17 April 2009
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In the author's paper [7] it was proved that the fractional parts of the partial sums of an infinite series (of real terms) diverging to +∞ or −∞, in which the general term tends to zero, are everywhere dense in the closed unit interval. This result was extended to series of infinite oscillation (see Remark 4.1 of the said paper) on the argument that a sequence of partial sums having infinite oscillation has a subsequence that diverges to +∞ or −∞.
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- Copyright © Australian Mathematical Society 1982
References
[1]Moorthy, S. Audinarayana, “Infinite series and the derived set of the aggregate of the fractional parts of its partial sums”, Bull. Austral. Math. Soc. 21 (1980), 253–264.CrossRefGoogle Scholar
[2]Pólya, G., Szegö, G., Problems and theorems in analysis. Volume I: Series, integral calculus, theory of functions (translated by Aeppli, D.. Die Grundlehren der mathematischen Wissenschaften, 193. Springer-Verlag, Berlin, Heidelberg, New York, 1972).Google Scholar
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