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

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Feng Qi
Qiu-Ming Luo


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.

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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.
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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