Compute the value of $1 - 2 + 3 - 4 + \dots + 2019 - 2020 + 2021$.

1 - 2 + 3 - 4 + ... + 2019 - 2020 + 2021 = 1007.

Compute the value of
\(1 - 2 + 3 - 4 + \dots + 2019 - 2020 + 2021\).

\(\begin{array}{|rcll|} \hline s &=& 1 - 2 + 3 - 4 + \dots + 2019 - 2020 + 2021 \\ s&=& 2021 - 2020 +2019 - \dots -4+3-2+1 \\ \hline 2s &=& 2022-2022+2022-2022 + \dots + 2022-2022+2022 \\ 2s &=& 0+0+ \dots +0+2022 \\ 2s &=& 2022 \\ s &=& 1011 \\ \hline \end{array}\)

\(1 - 2 + 3 - 4 + \dots + 2019 - 2020 + 2021 = \mathbf{1011} \)

heureka posted a great solution, so I will post a different one.

\(\quad1 - 2 + 3 - 4 + \cdots + 2019 - 2020 + 2021\\ =(1 - 2) + (3 - 4) + \cdots + (2019 - 2020) + 2021\\ = \underbrace{(-1) + (-1) + \cdots + (-1)}_{1010\text{ times}} + 2021\\ =-1010 + 2021\\ = 1011\)