（1+1/1997+1/1999+1/2001)×(1/1997+1/1999+1/2001+1/2003)-(1+1/1997+1/1999+1/2001+1/2003)×(1/1997+1/1999+1/2001)=[1+(1/1997+1/1999+1/2001)]×(1/1997+1/1999+1/2001+1/2003)-[1+(1/1997+1/1999+1/2001+1/2003)]×(1/1997+1/1999+1/2001)=1/1997+1/1999+1/2001

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 21:54:21
（1+1/1997+1/1999+1/2001)×(1/1997+1/1999+1/2001+1/2003)-(1+1/1997+1/1999+1/2001+1/2003)×(1/1997+1/1999+1/2001)=[1+(1/1997+1/1999+1/2001)]×(1/1997+1/1999+1/2001+1/2003)-[1+(1/1997+1/1999+1/2001+1/2003)]×(1/1997+1/1999+1/2001)=1/1997+1/1999+1/2001

（1+1/1997+1/1999+1/2001)×(1/1997+1/1999+1/2001+1/2003)-(1+1/1997+1/1999+1/2001+1/2003)×(1/1997+1/1999+1/2001)=[1+(1/1997+1/1999+1/2001)]×(1/1997+1/1999+1/2001+1/2003)-[1+(1/1997+1/1999+1/2001+1/2003)]×(1/1997+1/1999+1/2001)=1/1997+1/1999+1/2001
（1+1/1997+1/1999+1/2001)×(1/1997+1/1999+1/2001+1/2003)-(1+1/1997+1/1999+1/2001+1/2003)×(1/1997+1/1999+1/2001)=[1+(1/1997+1/1999+1/2001)]×(1/1997+1/1999+1/2001+1/2003)-[1+(1/1997+1/1999+1/2001+1/2003)]×(1/1997+1/1999+1/2001)=1/1997+1/1999+1/2001+1/2003-1/1997-/1999-1/2001=1/2003

（1+1/1997+1/1999+1/2001)×(1/1997+1/1999+1/2001+1/2003)-(1+1/1997+1/1999+1/2001+1/2003)×(1/1997+1/1999+1/2001)=[1+(1/1997+1/1999+1/2001)]×(1/1997+1/1999+1/2001+1/2003)-[1+(1/1997+1/1999+1/2001+1/2003)]×(1/1997+1/1999+1/2001)=1/1997+1/1999+1/2001
设1/1997+1/1999+1/2001=A
原式=(1+A)×(A+1/2003)-(1+A+1/2003)×A
=(A+1/2003)+A×(A+1/2003)-A-(A+1/2003)×A
=1/2003

你这个问题这样看就容易了。
设：a=1/1997+1/1999+1/2001；
原式（1+1/1997+1/1999+1/2001)×(1/1997+1/1999+1/2001+1/2003)-(1+1/1997+1/1999+1/2001+1/2003)×(1/1997+1/1999+1/2001)
=[1+（1/1997+1/1999+1/2001)]×[(1/1997...

全部展开

你这个问题这样看就容易了。
设：a=1/1997+1/1999+1/2001；
原式（1+1/1997+1/1999+1/2001)×(1/1997+1/1999+1/2001+1/2003)-(1+1/1997+1/1999+1/2001+1/2003)×(1/1997+1/1999+1/2001)
=[1+（1/1997+1/1999+1/2001)]×[(1/1997+1/1999+1/2001）+1/2003)]
-[1+(1/1997+1/1999+1/2001）+1/2003]×(1/1997+1/1999+1/2001)
=（1+a）（a+1/2003）-（1+a+1/2003）a
=a+1/2003+a＾2+（1/2003）a-a+a＾2-（1/2003）a
=1/2003
看明白了吧？就是同类项整理。

收起

2000*1999-1999*1998+1998*1997-1997*1996+.+2*1 1+2+3+4+.+1997+1998+1999 1999*1999－（998*1998-（1997*1997-（1996*1996-.（2*2-1）.) 计算：2000*1999-1999*1998+1998*1997-1997*1996+.+2*1 2000*1999-1999*1998+1998*1997-1997*1996+.+2*1用简便方法求得数, 2000×1999-1999×1998＋1998×1997-1997×1996＋…＋2×1 2000乘1999-1999乘1998+1998乘1997-1997乘1996+.2乘1 2000*1999-1999*1998+1998*1997-1997*1996+...+2*1= (1996+95*1997)/(1996*1997-1)+(1997+1996*1998)/(1997*1998-1)+(1998+1997*1999)/(1998*1999-1) （1999+1991/1999）×1/4 —1997/1999=? 1/(1996*1997)+1/(1997*1998)+1/(1998*1999)+1/(1999*2000)+1/2000 （1+1/1997+1/1999+1/2001)×(1/1997+1/1999+1/2001+1/2003)-(1+1/1997+1/1999+1/2001+1/2003)×(1/1997+1/1999+1/2001)=[1+(1/1997+1/1999+1/2001)]×(1/1997+1/1999+1/2001+1/2003)-[1+(1/1997+1/1999+1/2001+1/2003)]×(1/1997+1/1999+1/2001)=1/1997+1/1999+1/2001 1/2+1/3+1/4+……+1/1997+1/1998+1/1999 1997+1996*1998/1997*1998-1+1998+1997*1999/1998*1999-1+1999+1998*2000/1999*2000 （1-1/2+1/3-1/4.+1/1997-1/1998+1/1999)/[1/(1+1999)+1/(2+2000)+1/(3+2001).+1/(999+2997)+1/(1000+2998)] 2000+1999-1998+1997-1996+.+3-2+1 1+2+3+.+1997+1998+1999等于多少 1-2+3-4+```+1997-1998+1999等于多少