2. Find the value of the expression

$$
2^{2}+4^{2}+6^{2}+\ldots+2018^{2}+2020^{2}-1^{2}-3^{2}-5^{2}-\ldots-2017^{2}-2019^{2}
$$
# Solution.

$$
\begin{aligned}
& 2020^{2}-2019^{2}+2018^{2}-2017^{2}+\ldots+6^{2}-5^{2}+4^{2}-3^{2}+2^{2}-1^{2}= \\
& =(2020-2019)(2020+2019)+(2018-2017)(2018+2017)+\ldots+ \\
& +(6-5)(6+5)+(4-3)(4+3)+(2-1)(2+1)= \\
& =2020+2019+2018+2017+\ldots+6+5+4+3+2+1= \\
& =\frac{2020+1}{2} \cdot 2020=2041210
\end{aligned}
$$

Answer. 2041210.