在-1/2,-1/3.-1/100中选出10个数,使他们的和等于-1

题目

在-1/2,-1/3.-1/100中选出10个数,使他们的和等于-1
RT

答案

-1
=-(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+1/8-1/9+1/9-1/10+1/10)
=-[(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)+(1/8-1/9)+(1/9-1/10)+1/10]
=-(1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/10)
所以这10个数分别是：-1/2、-1/6、-1/10、-1/12、-1/20、-1/30、-1/42、-1/56、-1/72、-1/90.