Proving the series $s_n=1+\frac{1}{\sqrt2}+\cdots +\frac{1}{\sqrt n}$ is not bounded
Other Idea to show an inequality $\dfrac{1}{\sqrt 1}+\dfrac{1}{\sqrt 2}+\dfrac{1}{\sqrt 3}+\cdots+\dfrac{1}{\sqrt n}\geq \sqrt n$