|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2006-1/2005|

来源：百度知道编辑：UC知道时间：2024/06/17 17:55:25

因为1/3<1/2
所以1/3-1/2<0
|1/3-1/2|=1/2-1/3
其他同理

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+......+|1/2006-1/2005|
=（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+……（1/2005/-1/2006）
=1/2-1/3+1/3-1/4+1/4-1/5+……1/2005/-1/2006
=1/2-1/2006
=501/1003

把绝对值号去掉就会了

(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1) 1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100) 1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100) 1+1/2+1/3+.....+1/n 1+1/2+1/3+...+1/100 1-1/2+1/3-.....-1/10 (1+1/2+1/3+1/4)× 1+1/1+2+1/1+2+3+...+1/1+2+3...+2000 1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=? (1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)