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A general form of Alzer's inequality

✍ Scribed by Zengkun Xu; Dapeng Xu

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
434 KB
Volume
44
Category
Article
ISSN
0898-1221

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✦ Synopsis

Let {u,,}?=~ be a strictly increasing positive sequence, and let m be a natural number and r a positive number. In this paper, we prove n-1 ll(n-1) an -< ( > il=', ai an+1 -( > fi@ l/n ' i=l for n 2 2, then < for 71 1 1.

An open problem proposed in [l], which concerns the sequence of natural numbers and might be a generalization of Alzer's inequality, is shown to be a special case of our second result. Relative results are also given.

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