UC知道1/2+1/6+1/12+1/20+1/30+1/42=
来源：百度知道 编辑：UC知道 时间：2024/05/29 01:23:45
1/2=1/1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
1/42=1/6-1/7
以上相加:
1-1/7=6/7
这叫裂项求和
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
...
1/42-1/6-1/7
原式=1-1/2+1/2-1/3+...+1/6-1/7
=6/7
1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7 =6/7
1/2+1/6+1/12+1/20+1/30+1/42=(210+70+35+14+10)/420=339/420=113/140
(1/2) (1/4+1/6)=
1/2+1/4+1/6+1/8+.......+1/n=?
1/2*4+1/4*6+1/6*8+.......+1/2006*2008
1/2*4+1/4*6+1/6*8+1/48*50
|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+....+|1/2006-1/2004|
|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+.....+|1/2006-1/2004|
|1/4-1/2|+|1/6-1/4|+|1/8-1/6|+```+|1/2008-1/2006|
(1-1/2)*(1-1/4)*(1-1/6)*...........*(1-1/10)解法
(1/2-1)*(1/3-1)*(1/4-1)*(1/5-1)*(1/6-1)*(1/7-1)*(1/8-1)*(1/9-1)*(1/10-1)
1/2+1/3+1/4+1/5+1/6+....+1/n=?