I've to resolve a inequality using the induction: for every natural number $\geq 1$
$$ \sum_{k=1}^n \frac{1}{\sqrt{k}} \geq \sqrt{n} $$
At the end, I arrive at this result, but I don't know how I can continue: $\sqrt{n}+1/\sqrt{n+1} \geq \sqrt{n+1}$