六年级的奥数简便计算（是分数的）有规律的

2025-03-04 13:37:13

推荐回答（3个）

回答1：

举个例子
1/(1*2)+1/(2*3)+1/(3*4)+......+1/(99*100)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+......(1/99-1/100)
=1-1/100
=99/100

回答2：

题太多了，举例说明
1/2+1/6+1/12+1/20+1/30+1/42
=（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+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7

回答3：

1/2+1/6+1/12+1/20+1/30+1/42
=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