Question

1/2,1/3,1/4,1/5,…,1/90,1/91,你能从中挑出十个,加上正负号,使它们的和等于-1

Answer 1

解这种题,一般首先是找出满足结果的和,不管有多少组,然后剩下的可以通过对消得0.

-1/2-1/3-1/6=-1

还差7个数

1/4-(1/8+1/12+1/24)=0

1/10-(1/15+1/30)=0

=>-1/2-1/3-1/6-1/4+1/8+1/12+1/24-1/10+1/15+1/30=-1

1/8-(1/12+1/24)=0

1/5-(1/10+1/15+1/30)=0

=>-1/2-1/3-1/6-1/8+1/12+1/24-1/5+1/10+1/15+1/30=-1

1/6=1/4-1/12

1/7-(1/8+1/56)=0

1/9-(1/10+1/90)=0

=>-1/2-1/3-1/4+1/12-1/7+1/8+1/56-1/9+1/10+1/90=-1

.

更多的可以自己组合了