1-1/2+1/6+1/12+1/20+1/30怎么简算

1-1/2+1/6+1/12+1/20+1/30怎么简算
1-1/2+1/6+1/12+1/20+1/30怎么简算

1-1/2+1/6+1/12+1/20+1/30怎么简算
认真观察一下,前四个数可以一步一步的算,因为分母都是倍数关系,算完之后是9/12,也就是3/4,然后通分加上1/20,是16/20,是4/5.再和1/30计算.是5/6.或者直接通分,分母是公倍数60,再计算.分子是（60-30+10+5+3+2）=50 结果是5/6.没有什么深层意思了吧?

1-1/2+1/6+1/12+1/20+1/30
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6
=5/6

1-1/2+1/6+1/12+1/20+1/30
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6
=5/6