1/( )+1/( )+1/( )+1/( )+1/( )+1/( )+1/( )=1,( )里填入7个互不相等且小于20的自然数,使等式成立

题目

1/( )+1/( )+1/( )+1/( )+1/( )+1/( )+1/( )=1,( )里填入7个互不相等且小于20的自然数,使等式成立

答案

1=1/2+1/2
=1/2+(1/3+1/6)
=1/3+1/6+(1/4+1/12)+(1/9+1/18)
=1/3+1/6+1/5+1/20+1/12+1/9+1/18
∴1/3+1/5+1/6+1/9+1/12+1/18+1/20=1.