Question

1到100自然数里任意抽取10个自然数.让这10个自然数的倒数之和为1

Answer 1

1/2+1/2=1

1/4+1/4=1/2

1/8+1/8=1/4.

1/2=1/3+1/6,1/32=1/48+1/96

按照这些思路找,很快凑到10个:

1=1/2+1/4+1/8+1/16+1/32+1/48+1/96

=1/3+1/6+1/4+1/8+1/16+1/32+1/48+1/96

=1/3+1/9+1/27+1/54+1/4+1/8+1/16+1/32+1/48+1/96