Question

若a,b,c,d都是互不相等的自然数,且满足1/a+1/b+1/c+1/d=1/2,则1/a+1/b+1/c+1/d可以

Answer 1

有如下恒等式

1-1/4=(1-1/2)+(1/2-1/3)+(1/3-1/4)=1/2+1/6+1/12

所以1=1/2+1/4+1/6+1/12

1/2=1/4+1/8+1/12+1/24