I ran into this limit while evaluating an integral.

$\underset{N\to \mathrm{\infty}}{lim}(2\sqrt{N+1}\phantom{\rule{thickmathspace}{0ex}}-\phantom{\rule{thickmathspace}{0ex}}\sum _{n=1}^{N}\frac{1}{\sqrt{n}})$

$\underset{N\to \mathrm{\infty}}{lim}(2\sqrt{N+1}\phantom{\rule{thickmathspace}{0ex}}-\phantom{\rule{thickmathspace}{0ex}}\sum _{n=1}^{N}\frac{1}{\sqrt{n}})$