$$
2015 \times 2016
$$
1. (8 points) The calculation result of the expression $\frac{1}{1+\frac{1}{2016}}+\frac{2}{2+\frac{2}{2016}}+\frac{3}{3+\frac{3}{2016}}+\cdots+\frac{2015}{2015+\frac{2015}{2016}}$ is
2017
【Solution】:
$$
\frac{2015 \times 2016}{\frac{1}{1+\frac{1}{2016}}+\frac{2}{2+\frac{2}{2016}}+\frac{3}{3+\frac{3}{2016}}+\cdots+\frac{2015}{2015+\frac{2015}{2016}}}
$$
$$
\begin{array}{l}
=\frac{2015 \times 2016}{2015 \text { terms }} \\
=\frac{2015 \times 2016}{\frac{1}{1+\frac{1}{2016}} \times 2015} \\
=2016 \times\left(1+\frac{1}{2016}\right) \\
=2017 ;
\end{array}
$$

Therefore, the answer is: 2017.