Limit of a sum $\frac{1}{\sqrt n}$ [duplicate]
Solution 1:
The sum has $n$ terms and each term is bounded from below by $\frac{1}{\sqrt{n}}$, so the sum is bounded from below by $\frac{n}{\sqrt{n}} = \sqrt{n}$. Of course, $\lim_{n \to \infty} \sqrt{n} = +\infty$.
(Using integrals or sophisticated criteria is an overkill in this case.)