2012²-2011²+2010²-2009²8······+2²-1²
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/26 19:44:00
2012²-2011²+2010²-2009²8······+2²-1²
2012²-2011²+2010²-2009²8······+2²-1²
2012²-2011²+2010²-2009²8······+2²-1²
=(2012+2011)*(2012-2011)+(2010+2009)*(2010-2009)+...+(2+1)*(2-1)
=2012+2011+2010+...+2+1
=[2012*(1+2012)]/2
=2013*1006
=2025078
2012²-2011²+2010²-2009²8······+2²-1²
=(2012-2011)(2012+2011)+(2010-2009)(2010+2009)+...+(2-1)(2+1)
=4023+4019+……3
=(4023+3)*1006/2=2025078