[tex]1 - 2 + 3 - 4 + 5 - 6 + ... + 2021 - 2022 = [/tex]
[tex](1 + 3 + 5 + ...2021) - 2( 1 + 2 +3 + ... + 1011) = [/tex]
[tex](0 \times 2 + 1) + (1 \times 2 + 1) + ... +( 2 \times 1010 + 1) - 2 \times \frac{1011 \times 1012}{2} = [/tex]
[tex]2 \times (0 + 1 + ... + 1010) + 1 + 1 + ... + 1 - 1011 \times 1012 = [/tex]
[tex]2 \times \frac{1010 \times 1011}{2} + 1 \times 1011 - 1011 \times 1012 = [/tex]
[tex]1010 \times 1011 + 1011 - 1011 \times 1012 = [/tex]
[tex]1011 \times (1010 + 1 - 1012) = [/tex]
[tex]1011 \times ( - 1) = - 1011[/tex]
