Generalization of H. Minc and L. Sathre's inequality
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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.
$${n+k\over n+m+k}<{{\root n\of {(n+k)!/k!}}\over {\root {n+m}\of {(n+m+k)!/k!}}}<1.$$
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. https://doi.org/10.5556/j.tkjm.31.2000.406
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