2,5,12,20,30,42,56的最小公倍数

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/

1又1/2－5/6+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/

3/2-5/6+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+

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+1/6-1/7-1/8+1/8+1/9=1+1/9=10/9

1+1/2-5/6+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+1/8=1+1/8=9/

=(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

每个加数都写成（1-一个数）原式=6-（1/2+1/6+1/12+...1/42)1/6=1/2-1/31/12=1/3-1/4...1/42=1/6-1/7

=7.1071428571428571428571428571429附件->计算器

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+

采纳我告诉你再答：再答：拜托采纳好不

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

=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+

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+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/

1/2+5/6+11/12+19/20+29/30+41/42=?=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)+(1-1/42)=6-(1/2+1/6+1/1

最后结果是1/8  请理解哦  如果满意 请采纳

列数据：a1=2a2=2+4=2*3a3=2+4+6=3*4a4=2+4+6+8=4*5a5=2+4+6+8+10=5*6一般性推导：an=2+4+6+8+10+...+2n=2(1+2+3+4+5+

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/

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

36/7裂项相消=6-(1/2+1/6+1/12+1/20+1/30+1/42)=6-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7)=6-6/7=36/