2 results
THE FLOOR OF THE ARITHMETIC MEAN OF THE CUBE ROOTS OF THE FIRST
$n$ INTEGERS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 102 / Issue 2 / October 2020
- Published online by Cambridge University Press:
- 08 January 2020, pp. 261-267
- Print publication:
- October 2020
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- Article
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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.
Telescoping Estimates for Smooth Series
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- Journal:
- Canadian Mathematical Bulletin / Volume 58 / Issue 1 / 01 March 2015
- Published online by Cambridge University Press:
- 20 November 2018, pp. 188-195
- Print publication:
- 01 March 2015
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- Article
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