1. Simplify:
$$
\sum_{k=1}^{2016}(k \sqrt{k+1}+(k+1) \sqrt{k})^{-1}=
$$
$-1.1-\frac{1}{\sqrt{2017}}$.
Notice that,
$$
\begin{array}{l}
(k \sqrt{k+1}+(k+1) \sqrt{k})^{-1} \\
=\frac{\sqrt{k+1}-\sqrt{k}}{\sqrt{k(k+1)}}=\frac{1}{\sqrt{k}}-\frac{1}{\sqrt{k+1}} .
\end{array}
$$

Therefore, the required result is $1-\frac{1}{\sqrt{2017}}$.