Generalization of H. Minc and L. Sathre's inequality

Authors

  • Feng Qi
  • Qiu-Ming Luo

DOI:

https://doi.org/10.5556/j.tkjm.31.2000.406

Abstract

An inequality of H. Minc and L. Sathre (Proc. Edinburgh Math. Soc. ${\bf 14}$(1964/65), 41-46) is generalized as follows: Let $n$ and $m$ be natural numbers, $k$ a nonnegative integer, then we have
$${n+k\over n+m+k}<{{\root n\of {(n+k)!/k!}}\over {\root {n+m}\of {(n+m+k)!/k!}}}<1.$$
From this, some corollaries are deduced. At last, an open problem is proposed.

Author Biographies

Feng Qi

Department of Mathematics, Jiaozuo Institute of Technology, Jiaozuo City, Henan 454000, China.

Qiu-Ming Luo

Department of Broadcast-Television Teaching, Jiaozuo University, Jiaozuo City, Henan 454151, China.

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Published

2000-06-30

How to Cite

Qi, F., & Luo, Q.-M. (2000). Generalization of H. Minc and L. Sathre’s inequality. Tamkang Journal of Mathematics, 31(2), 145-148. https://doi.org/10.5556/j.tkjm.31.2000.406

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Papers

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