1²-2²+3²-4²+...+2003²-2004²+2005²-2006²+2007²=
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 07:23:04
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1²-2²+3²-4²+...+2003²-2004²+2005²-2006²+2007²=
1²-2²+3²-4²+...+2003²-2004²+2005²-2006²+2007²=
1²-2²+3²-4²+...+2003²-2004²+2005²-2006²+2007²=
1²-2²+3²-4²+...+2003²-2004²+2005²-2006²+2007²
=1²+(3²-2²)+(5²-4²)+…+(2007²-2006²)
=1+(3+2)(3-2)+(5-4)(5+4)+…+(2007-2006)(2007+2006)
=1+2+3+4+5+…+2007
=2007×2008/2
=2015028