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An extension of a result of Sierpiński

✍ Scribed by M.A. Nyblom

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
231 KB
Volume
105
Category
Article
ISSN
0022-314X

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✦ Synopsis

As an application of Roth's theorem concerning the rational approximation of algebraic numbers, two sufficiency conditions are derived for an alternating series of rational terms to converge to a transcendental number. The first of these conditions represents an extension of an earlier condition of Sierpin´ski for the convergence of alternating series to irrational values.

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