[问答题]
1. Show that $\frac{1}{2 \sqrt{n+1}}<\sqrt{n+1}-\sqrt{n}$ , where $ \in \mathbb{Z}$, $n \geq 0$ .
2. Hence show that $\frac{1}{\sqrt{2}}<2 \sqrt{2}-2$ .
3. Prove by mathematical induction that
$\sum_{r=2}^{n} \frac{1}{\sqrt{r}}<2 \sqrt{n}-2 \quad $ for all $ n \in \mathbb{Z}^{+}, n \geq 2$
