2010²-2009²+2008²-2007²+2006²+.+2²-1²=
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 23:49:04
![2010²-2009²+2008²-2007²+2006²+.+2²-1²=](/uploads/image/z/169765-61-5.jpg?t=2010%26%23178%3B-2009%26%23178%3B%2B2008%26%23178%3B-2007%26%23178%3B%2B2006%26%23178%3B%2B.%2B2%26%23178%3B-1%26%23178%3B%3D)
2010²-2009²+2008²-2007²+2006²+.+2²-1²=
2010²-2009²+2008²-2007²+2006²+.+2²-1²=
2010²-2009²+2008²-2007²+2006²+.+2²-1²=
原式=(2010+2009)(2010-2009)+(2008+2007)(2008-2007)…+(2+1)(2-1)
=2010+2009+2008+2007…+2+1
=(2010+1)×1005=2021055