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THE FLOOR OF THE ARITHMETIC MEAN OF THE CUBE ROOTS OF THE FIRST INTEGERS
Bulletin of the Australian Mathematical Society ( IF 0.6 ) Pub Date : 2020-01-08 , DOI: 10.1017/s0004972719001412 BOONYONG SRIPONPAEW , SOMKID INTEP
Bulletin of the Australian Mathematical Society ( IF 0.6 ) Pub Date : 2020-01-08 , DOI: 10.1017/s0004972719001412 BOONYONG SRIPONPAEW , SOMKID INTEP
Zacharias [‘Proof of a conjecture of Merca on an average of square roots’, College Math. J. 49 (2018), 342–345] proved Merca’s conjecture that the arithmetic means $(1/n)\sum _{k=1}^{n}\sqrt{k}$ of the square roots of the first $n$ integers have the same floor values as a simple approximating sequence. We prove a similar result for the arithmetic means $(1/n)\sum _{k=1}^{n}\sqrt[3]{k}$ of the cube roots of the first $n$ integers.
中文翻译:
第一个整数的三次方根的算术平均值的下限
Zacharias ['关于平均平方根的 Merca 猜想的证明',大学数学。J。 49 (2018), 342–345] 证明了 Merca 的猜想,即算术平均值$(1/n)\sum _{k=1}^{n}\sqrt{k}$ 第一个的平方根$n$ 整数与简单的近似序列具有相同的底值。我们证明了算术平均值的类似结果$(1/n)\sum _{k=1}^{n}\sqrt[3]{k}$ 第一个的立方根$n$ 整数。
更新日期:2020-01-08
中文翻译:
第一个整数的三次方根的算术平均值的下限
Zacharias ['关于平均平方根的 Merca 猜想的证明',