计算:1²-2²+3²-4²+.+99²-100²
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/28 23:30:42
计算:1²-2²+3²-4²+.+99²-100²
![计算:1²-2²+3²-4²+.+99²-100²](/uploads/image/z/8629664-32-4.jpg?t=%E8%AE%A1%E7%AE%97%3A1%26%23178%3B-2%26%23178%3B%2B3%26%23178%3B-4%26%23178%3B%2B.%2B99%26%23178%3B-100%26%23178%3B)
1²-2²+3²-4²+.+99²-100²=(1-2)(1+2)+(3-4)(3+4)+...+(99-100)(99+100)
=-(1+2)-(3+4)-.-(99+100)=-(1+2+3+4+...+99+100)=-(1+100)*50=-5050
=-(1+2)-(3+4)-.-(99+100)=-(1+2+3+4+...+99+100)=-(1+100)*50=-5050