A simple proof of generalized Alzer's inequality (Q1769900)
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scientific article; zbMATH DE number 2150500
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple proof of generalized Alzer's inequality |
scientific article; zbMATH DE number 2150500 |
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A simple proof of generalized Alzer's inequality (English)
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30 March 2005
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Let \(A(r,n)= {1\over n} \sum^n_{i=1} i^r\). In 1993 Alzer proved that \((A(r,n)/A(r,n+1))^{1/r}\geq n/(n+1)\). In 1995 the reviewer obtained a simple proof based on mathematical induction and Cauchy's mean value theorem. The authors offer a new proof based on induction and an auxiliary result which uses convex functions.
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inequalities for finite sums
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Alzer inequality
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