I tried to change it into a Riemann sum but failed, since
lim
which is not a standard form. Maybe, it need apply the squeeze theorem, but how to evaluate the bound.
By the way, WA gives its result
\begin{align*} \lim_{n \to \infty}\sum_{k=0}^n \frac{\sqrt{n}}{n+k^2}=\frac{\pi}{2}. \end{align*}
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