1/2*1/3+1/3*1/4+1/4*1/5+……1/2002*1/2003=1/2-1/3+1/3-1/4+1/4-.-1/2002+1/2002-1/2003

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/06 00:49:54

1/2*1/3+1/3*1/4+1/4*1/5+……1/2002*1/2003=1/2-1/3+1/3-1/4+1/4-.-1/2002+1/2002-1/2003
1/2*1/3+1/3*1/4+1/4*1/5+……1/2002*1/2003=1/2-1/3+1/3-1/4+1/4-.-1/2002+1/2002-1/2003

1/2*1/3+1/3*1/4+1/4*1/5+……1/2002*1/2003=1/2-1/3+1/3-1/4+1/4-.-1/2002+1/2002-1/2003
很简单的嘛
看式子
1/2n*1/2n+1=1/2n(2n+1)
1/2n-1/2n+1=1/2n(2n+1)
n>=1的整数
这样两边的式子就是相等的

1/N*（N+1）=1/N-1/（N+1）

1/n-1/(n+1)=(n+1-n)/n*(n+1)=1/n(n+1)

1/n*1/(n+1)=1/[n*(n+1)]=[(n+1)-n]/[n*(n+1)]=
1/n-1/(n+1)
明白了吗?

1/2*1/3+1/3*1/4+1/4*1/5+……1/2002*1/2003=1/2-1/3+1/3-1/4+1/4-......-1/2002+1/2002-1/2003
=1/2-1/2003
=2001/4006

(1+1/2+1/3+1/4+1/5)*(1/3+1/4+1)-(1+1/3+1/4)*(1/2+1/3+1/4+1/5) 1+2+3+4+1 (1+1/2+1/3+1/40)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4),不好意思,是下面这个! /1/3-1/2/+/1/4-1/3/+/1/5-1/4/+.+/1/10-1/9/ |1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2008-1/2007| |1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/10-1/9| 1/2 1/3 1/4是勾股数吗 1/3+1/2+1/4 1/2*1/3*1/4 1/2+1/3+1/4=? 1/2-3/1-4/1= 1 2 3 4 1 2 3 4 1 2 3 4 1,2,3,4, 1 2 3 4 1 2 3 4 1,2,3,4,