1^2-2^2+3^2-4^2+5^2-6^2+……+99^2-100^2
=(1+2)(1-2)+(3+4)(3-4)+......+(99+100)(99-100)
=-(1+2)-(3+4)-......-(99+100)
=-(1+2+3+4+...+99+100)
=-5050
1^2-2^2+3^2-4^2+5^2-6^2+...+99^2-100^2=
(1^2-2^2)+(3^2-4^2)+(5^2-6^2)+...+(99^2-100^2)=
(1-2)(1+2)+(2-3)(2+3)+(3-4)(3+4)+...+(99-100)(99+100)=
-(1+2)-(2+3)-(3+4)-...-(99+100)=
-(1+2+3+..+100)=
-50(1+100)=
-5050
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