1/2+1/6+1/12+1/20+…+1/90=

来源：百度知道编辑：UC知道时间：2024/06/28 11:04:39

=1/1*2+1/2*3+1/3*4+……+1/9*10
=1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10
中间正负抵消
=1-1/10
=9/10

1 / 2 + 1 / 6 + 1 / 12 + 1 / 20 + … + 1 / 90
= 1 / (1 * 2) + 1 / (2 * 3) + 1 / (3 * 4) + … + 1 / (9 * 10)
= (1 - 1 / 2) + (1 / 2 - 1 / 3) + (1 / 3 - 1 / 4) + … + (1 / 9 - 1 / 10)
= 1 + (- 1 / 2 + 1 / 2) + (- 1 / 3 + 1 / 3) + … + (- 1 / 9 + 1 / 9) - 1 / 10
= 1 - 1 / 10
= 9 / 10 .

1/2+1/6+1/12+1/20+…+1/90
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+-----+1/9-1/10
=1-1/10
=9/10

1/2+1/6+1/12+1/20+…+1/90
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+···+1/9-1/10
=1-1/10
=9/10

(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=?