3,12,20,30,42,56,72,90的最小公倍数

5/6+5/12+5/20+5/30+5/42+5/56+5/72=5×（1/2-1/3+1/3-1/4+……+1/8-1/9）=5×（1/2-1/9）=5×7/18=35/18

这题我来解答.如果是用裂项做,那么,观察分数,前三个无法裂项,从第四项开始7/12+9/20+11/28+17/30+25/42中,每个分数的分母都是偶数,由此有,7/12=7/(3*4)=7*(1/

5/6-7/12+9/20-11/30+13/42=(1/2+1/3)-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)=1/2+1/3-1/3-1/4+1/4+1/5-

3/2-5/6+7/12-9/20+11/30-13/42=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)=1+1/2-1/2-1/3+

1.原式=1-2+3-4+5-6+7-8+9+1/2-5/6+1/12-19/20+1/30-41/42+1/56-71/72+1/90=5+1/2-5/6+1/12-19/20+1/30-41/42

=(1+1/2)-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+1

3/2-5/6+7/12-9/20+11/30-13/42=1＋1/2-1/2-1/3＋1/3＋1/4-1/4-1/5＋1/5＋1/6-1/6-1/7内部全部抵消.=1-1/7=6/7

2/3-5/6+7/12-9/20+11/30-13/42=2/3-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)=2/3-1/2-1/3+1/3+

=3/2-5/6+7/12-9/20+11/30-13/42+15/56=(1+1/2)-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+

3/5+6/7+7/12+9/20+11/30+13/42=(3*4*6*7+6*4*5*6+7*2*5*7+9*6*7+11*4*7+13*4*5)/(4*5*6*7)=2660/840=19/6

0.710.20.290.531.61.21.82再问：那24/75呢再答：0.32

3,6,12,20,30,42,（56）,（72）除了第一项不符合,后面应该通项为n（n+1)最后一列是1,1,3,5,9,（17）,（31）前面连续三项和等于接下来的第四项再问：1,8,27,(),

2/3-5/6+7/12-9/20+11/30-13/42=(1-1/3)-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)=1-1/3-1/2-1/

5/3+7/6+6/5+12/7+20/9+30/11+42/13=5/3+7/6+6/5+3/1+4/1+4/1+5/1+5/1+6/1+6/1+7/1=（7/6+7/1）+（5/3+5/1+5/1

3/2-5/6+7/12-9/20+11/30-13/42=（1+1/2）-（1/2+1/3）+（1/3+1/4）-（1/4+1/5）+（1/5+1/6）-（1/6+1/7）=1-1/7=6/7如果本

3/5+6/7+5/6+7/12+9/20+11/30+13/42=3/5+6/7+5/6+1/3+1/4+1/4+1/5+1/5+1/6+1/6+1/7=(3/5+1/5+1/5)+(6/7+1/7

3/2-5/6+7/12-9/20+11/30-13/42=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)=1+1/2-1/2-1/3+

拆数5/6=2/6+3/6=1/3+1/21/12=4/12-3/12=1/3-1/49/20=4/20+5/20=1/5+1/411/30=5/30+6/30=1/6+1/51/42=7/42-6/

9/8

题目都写错...3/2-5/6+7/12-9/20+11/30-13/42+15/56=1+1/2-1/2-1/3+1/3+1/4……+1/7+1/8=1又1/8