UC知道1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+...+1/(9*10)
来源：百度知道 编辑：UC知道 时间：2024/07/02 09:31:44
小学六年级数学思维拓展
[1/(2*3)+1/(3*4)]+....+[1/(8*9)+1/(9*10)]=1/4+1/12+1/24+1/40=6/24+2/24+1/24+1/40=9/24+1/40=3/8+1/40=15/40+1/40=16/40=2/5
解：原式=（1/2-1/3）+（1/3-1/4）……-1/9+1/9-1/10
=1/2-1/10
=2/5
1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10=1/2-1/10=2/5
1/(2*3)=1/2-1/3，依次类推
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)
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)
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+2+3 +....+ 1/1+2+3+....+100=