n為大于1的自然數(shù)
可以用數(shù)學(xué)歸納法來證：
（1）當(dāng)n=2時
1/(2+1)+1/(2+2)=1/3+1/4=7/12=14/24>13/24成立
（2）假設(shè)當(dāng)n=k時成立
即：1/(k+1)+1/(k+2)+1/(k+1)+---+1/(k+k)>13/24
那么當(dāng)n=k+1時
1/(k+2)+1/(k+1)+---+1/(k+k)+1/(2k+1)+1/(2k+2)
=1/(k+1)+1/(k+2)+1/(k+1)+---+1/(k+k)+1/(2k+1)+1/(2k+2)-1/(k+1)
>13/24+1/(2k+1)+1/(2k+2)-1/(k+1)
>13/24+1/(2k+2)+1/(2k+2)-2/(2k+2)=13/24
說明當(dāng)n=k+1時也成立
由（1）（2）可知不等式對于大于1的自然數(shù)都成立