1²-2²+3²-4²+5²-6²+7²-8²+9²……+99²-100²=

问题描述:

1²-2²+3²-4²+5²-6²+7²-8²+9²……+99²-100²=

(1+2)*(1-2) + (3+4)*(3-4) + ... + (99+100)*(99-100)
= - ( 1+2+3+4+...+100 ) = -5050

1²-2²+3²-4²+5²-6²+7²-8²+9²……+99²-100²
=(1-2)(1+2)+(3-4)(3+4)+(5-6)(5+6)+……+(99-100)(99+100)
=-(1+2+3+4+……+99+100)
=-100/2*(1+100)
=-5050