Question

从1到100个正整数中,取出10个,使其倒数的和等于1,求这10个数

Answer 1

2,6,12,20,30,42,56,72,90,10

因为1/[n（n+1）]=1/n-1/(n+1)

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/10

=1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10+1/10

=1-1/10+1/10

=1