1²-2²+3²-4²+5²-6²+7²-8²+9²……+99²-100²=
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/23 21:50:20
![1²-2²+3²-4²+5²-6²+7²-8²+9²……+99²-100²=](/uploads/image/z/673460-44-0.jpg?t=1%26%23178%3B-2%26%23178%3B%2B3%26%23178%3B-4%26%23178%3B%2B5%26%23178%3B-6%26%23178%3B%2B7%26%23178%3B-8%26%23178%3B%2B9%26%23178%3B%E2%80%A6%E2%80%A6%2B99%26%23178%3B-100%26%23178%3B%3D)
1²-2²+3²-4²+5²-6²+7²-8²+9²……+99²-100²=
1²-2²+3²-4²+5²-6²+7²-8²+9²……+99²-100²=
1²-2²+3²-4²+5²-6²+7²-8²+9²……+99²-100²=
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
(1+2)*(1-2) + (3+4)*(3-4) + ... + (99+100)*(99-100)
= - ( 1+2+3+4+...+100 ) = -5050