Ta có:
2018^2 - 2017^2 = (2018+2017)(2018-2017) = 2018+2017
2016^2 - 2015^2 = (2016+2015)(2016-2015)=2016+2015
...
2^2-1^2 = (2+1)(2-1) = 2+1
khi đó : 2018^2-2017^2+2016^2-2015^2+...+2^2-1^2
= (2018^2-2017^2 ) + ( 2016^2-2015^2 ) +.... + (2^2-1^2)
= 2018+2017+2016+2015+...+2+1
= $\frac{2018.(1+2018)}{2}$
= 2037171.