作业帮2012²-2011²+2010²-2009²8······+2²-1²
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/03 03:35:36
x
0 ABI4Sh+BA ` T aV@W M/ g?;Ff\IWb~6= ҈=_ra»<óHZ%
Q#G4e d!X91z\K,DX 5Sv֟.]"A,/2ym "C/0V*&lp5;
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