I. Fill-in-the-blank Questions (8 points each, total 64 points)
1. Let the sequence $\left\{\frac{1}{(n+1) \sqrt{n}+n \sqrt{n+1}}\right\}$ have the sum of its first $n$ terms as $S_{n}$. Then the number of rational numbers in the first 2016 terms of the sequence $\left\{S_{n}\right\}$ is $\qquad$.
$-1.43$
From $\frac{1}{(n+1) \sqrt{n}+n \sqrt{n+1}}=\frac{\sqrt{n}}{n}-\frac{\sqrt{n+1}}{n+1}$ $\Rightarrow S_{n}=1-\frac{\sqrt{n+1}}{n+1}$.
Since $44<\sqrt{2016}<45$, the number of $n$ that makes $S_{n}$ a rational number is 43.