# Mircea Merca's conjecteture

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?

• The asymptotic behaviour of $H_n^{(1/2)}$ can be found by summation by parts or creative telescoping. This is more a challenging exercise in Calculus than a ground-breaking conjecture. – Jack D'Aurizio Nov 18 '18 at 0:04
• This is OEIS sequence A300287 which has a link to Thomas P. Wihler, arXiv:1803.00362. – Somos Nov 18 '18 at 0:18