Ta có:
` 1^2 - 2^2 + 3^2 - 4^2 + ... + 2017^2 - 2018^2 + 2019^2 `
` = 1 + (-2^2 + 3^2) + (-4^2 + 5^2) + ... + (-2016^2 + 2017^2) + (-2018^2 + 2019^2) `
` = 1 + (3 - 2)(3 + 2) + (5 - 4)(5 + 4) + ... + (2017 - 2016)(2017 + 2016) + (2019 - 2018)(2019 + 2018) `
` = 1 + 5 + 9 + ... + 4033 + 4037 `
` = \frac{4037+1}{2} . 1010 `
` = 2039190 `