2010*2010-2009*2009+2008*2008···················+2*2-1*1楼1回答看不懂...

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/21 14:54:25
2010*2010-2009*2009+2008*2008···················+2*2-1*1楼1回答看不懂...2010*2010-2009*2009+2008*2008·····

2010*2010-2009*2009+2008*2008···················+2*2-1*1楼1回答看不懂...
2010*2010-2009*2009+2008*2008···················+2*2-1*1
楼1回答看不懂...

2010*2010-2009*2009+2008*2008···················+2*2-1*1楼1回答看不懂...
原式=(2010的平方-2009的平方)+.+(2的平方-1的平方)
到这步时,用一下平方差公式,这个初一书上就有,用完这个公式,变成了
=【(2010+2009)(2010-2009)】+【(2008+2007)(2008-2007)】+.+【(2+1)(2-1)】
到这步时,发现2010-2009,2008-2007,.,2-1结果均为1
=(2010+2009)+(2008+2007)+.+(2+1)
到这步时,就很简单啦,不就成了1+2+3+.+2010了吗,用一下等差数列求和公式(不知道的话,百度搜一下,很简单)
=(1+2010)*2010/2=2021055

2010*2010-2009*2009+2008*2008............+2*2-1*1
=(2010+2009)*(2010-2009)+(2008+2007)*(2008-2007)...........+(2+1)*(2-1) 平方差公式两项一组
=(2010+2009)*1+(2008+2007)*1.........(2+1)*1
=2010+2009+.....+2+1
=(2010+1)*2010/2 等差数列求和公式
=2020050

2010*2010-2009*2009+2008*2008···················+2*2-1*1
=2010*(2009+1)-2009*2009+2008*2008···················+2*2-1*1
=2010*2009+2010*1-2009*2009+2008*2008···················+2*2-1*1
=201...

全部展开

2010*2010-2009*2009+2008*2008···················+2*2-1*1
=2010*(2009+1)-2009*2009+2008*2008···················+2*2-1*1
=2010*2009+2010*1-2009*2009+2008*2008···················+2*2-1*1
=2010*2009-2009*2009+2010*1+2008*2008···················+2*2-1*1
=2009*(2010-2009)+2010*1+2008*2008···················+2*2-1*1
=2009+2010+……(后面规律也这样)+……+2+1

收起

2010方-2009方+08方-07方。。。。。+2方-1方=(2010-2009)(2010+2009)...............=2010+2009+2008+2007.......................=(2010+1)*2010/2=2020050

原式=(2010+2009)*1+(2008+2007)*1+……+(2+1)*1
=2010+2009+……+2+1

=2010+2009+2008+......1
=(1+2010)*2010/2
=2021055