2011²-2010²+2009²-2008²+…+3²-2²+1²=---------
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/14 12:59:40
![2011²-2010²+2009²-2008²+…+3²-2²+1²=---------](/uploads/image/z/164397-21-7.jpg?t=2011%26%23178%3B%EF%BC%8D2010%26%23178%3B%EF%BC%8B2009%26%23178%3B%EF%BC%8D2008%26%23178%3B%EF%BC%8B%E2%80%A6%EF%BC%8B3%26%23178%3B%EF%BC%8D2%26%23178%3B%EF%BC%8B1%26%23178%3B%EF%BC%9D---------)
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2011²-2010²+2009²-2008²+…+3²-2²+1²=---------
2011²-2010²+2009²-2008²+…+3²-2²+1²=---------
2011²-2010²+2009²-2008²+…+3²-2²+1²=---------
2011²-2010²+2009²-2008²+…+3²-2²+1²
=(2011+2010)(2011-2010)+(2009+2008)(2009-2008)+(2007+2006)(2007-2006)+...+(3+2)(3-2)+1
=2011+2010+2009+2008+2007+2006+...+3+2+1
=2011×2012/2
=2023066