计算1^2-2^2+3^2-4^2+……+2007^2-2008^2
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/11/20 05:55:45
计算1^2-2^2+3^2-4^2+……+2007^2-2008^2
1^2-2^2+3^2-4^2+5^2-6^2+ ……+2007^2-2008^2
=(1^2-2^2)+(3^2-4^2)+(5^2-6^2)+……+(2007^2-2008^2)
=(1-2)(1+2)+(3-4)(3+4)+(5-6)(5+6)+……+(2007-2008)(2007+2008)
=-3-7-11-15-……-4011-4015
=-(3+4015)×1004/2
=2009×1004
=2017036
=(1^2-2^2)+(3^2-4^2)+(5^2-6^2)+……+(2007^2-2008^2)
=(1-2)(1+2)+(3-4)(3+4)+(5-6)(5+6)+……+(2007-2008)(2007+2008)
=-3-7-11-15-……-4011-4015
=-(3+4015)×1004/2
=2009×1004
=2017036