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ON PARTIAL SUMS OF SLOWLY DIVERGENT NUMERICAL SERIES

Dušan V. Slavić and Milan N. Tasić
Publikacije Elektrotehničkog fakulteta. Serija Matematika i fizika
No. 338/352 (1971), pp. 63-67
Stable URL: http://www.jstor.org/stable/43667516
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
ON PARTIAL SUMS OF SLOWLY DIVERGENT NUMERICAL SERIES
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Abstract

In this paper we analyse a class of slowly divergent numerical series whose partial sums are (1) $s\,(n,r)\, = \,\sum\limits_{k = 1}^n {a(k,r)} = \sum\limits_{k = 1}^n {\prod\limits_{p = 0}^r {\frac{1}{{\log {}_p(k\,{{\exp }_p}\,1)}}} } $ where k, n = 1, 2, ..., p, r = 0, 1, 2, ..., and log₀ x = x, logp+1 x = log (logp x), exp₀ x = x, expp+1 = exp (expp x). One of the obtained results is: For n → + ∞ $s\,(n,1)\, = \,\sum\limits_{k = 1}^n {\frac{1}{{k\,\log \,(ke)}} \to \log \left( {\log \left( {n + \frac{1}{2}} \right) + 1} \right) + {C_1}a(k,r)} $ where C₁ = 0.63985 . . . .

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