1. Calculate: $1^{2}-2^{2}+3^{2}-4^{2}+\ldots+2017^{2}$.
Solution: $1^{2}-2^{2}+3^{2}-4^{2}+\ldots+2017^{2}=$

$$
\begin{aligned}
& =\left(1^{2}-2^{2}\right)+\left(3^{2}-4^{2}\right)+\ldots+\left(2015^{2}-2016^{2}\right)+2017^{2}= \\
& =(1-2)(1+2)+(3-4)(3+4)+\ldots+(2015-2016)(2015+2016)+2017^{2}= \\
& =-(1+2)-(3+4)-\ldots-(2015+2016)+2017^{2}= \\
& =-(1+2+3+4+\ldots+2015+2016)+2017^{2}= \\
& =-\frac{1+2016}{2} \cdot 2016+2017^{2}=-2017 \cdot 1008+2017^{2}=2017 \cdot(2017-1008)= \\
& =2017 \cdot 1009=2035153
\end{aligned}
$$

Answer: 2035153.