1/2-1/6-1/12-1/20-1/30......-1/132=?

来源：百度知道编辑：UC知道时间：2024/06/15 12:52:41

1/2=1/(1*2)=1/1-1/2
1/6=1/(2*3)=1/2-1/3
...
1/132=1/(11*12)=1/11-1/12
左边相加，右边相加
1/2+1/6+...+1/132=1/1-1/2+1/2-1/3+....+1/11-1/12=11/12
(-1/2)+(-1/6)+（-1/12）+…+（-1/132）
=-(1-1/12)
=-11/12

1/2-1/6-1/12-1/20-1/30......-1/132=1-1/2+1/2-1/3......-1/132=131/132,中间可抵消

1/2=1/(1*2)=1/1-1/2
1/6=1/(2*3)=1/2-1/3
...

原式=1-1/2+1/2-1/3+……-1/132=131/132

(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=?