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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

S. Audinarayana Moorthy
S. Audinarayana Moorthy
Affiliation:
Department of Mathematics, Kendrapara College, Kendrapara 754 211, Cuttack Dt., Orissa, India.
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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 −∞.

Type
Addendum
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 2 , April 1982 , pp. 315 - 316
Copyright
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