Rounding the arithmetic mean value of the square roots of the first $n$ integers

Thomas P. Wihler

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arXiv · 1803.00362

Rounding the arithmetic mean value of the square roots of the first $n$ integers

Thomas P. Wihler

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Abstract

In this article we study the arithmetic mean value $\Sigma(n)$ of the square roots of the first $n$ integers. For this quantity, we develop an asymptotic expression, and derive a formula for its integer part which has been conjectured recently in the work of M. Merca. Furthermore, we address the numerical evaluation of $\Sigma(n)$ for large $n\gg 1$.

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Thomas P. Wihler. 2018-03-01. Rounding the arithmetic mean value of the square roots of the first $n$ integers. https://arxiv.org/abs/1803.00362

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