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:2024/07/03 02:01:28
![1²-2²+3²-4²+...+2003²-2004²+2005²-2006²+2007²=](/uploads/image/z/89197-61-7.jpg?t=1%26%23178%3B-2%26%23178%3B%2B3%26%23178%3B-4%26%23178%3B%2B...%2B2003%26%23178%3B-2004%26%23178%3B%2B2005%26%23178%3B-2006%26%23178%3B%2B2007%26%23178%3B%3D)
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