计算:1²-2²+3²-4²+.+99²-100²
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/06 13:10:02
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计算:1²-2²+3²-4²+.+99²-100²
计算:1²-2²+3²-4²+.+99²-100²
计算:1²-2²+3²-4²+.+99²-100²
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)(1-2)+(3+4)(3-4)+...+(99+100)(99-100)
=-(1+2+3+4+...+99+100)
=-(1+100)*100/2
=-5050