Mircea Merca conjectured that $$\left \lfloor{\frac{1}{n}\sum_{k=1}^n\sqrt{k}}\right \rfloor=\left \lfloor{\left(\frac{2}{3}+\frac{1}{6n}\right)\sqrt{n+1}}\right \rfloor$$ John Zacharias claimed that he had proved this conjecture in this article. Did he actually prove the conjecture? How can I find the related article?
2026-03-26 03:00:19.1774494019
Mircea Merca's conjecteture
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