证明：
当n=1时,a2=a1+(a1^2)/1^2=1/3+1/18=7/18>1/2-1/4=7/28成立
设n=k时,ak+1=ak+(ak^2)/(k^2)>1/2-1/4k成立
当n=k+1时,ak+2=ak+1+(ak+1^2)/(k+1)^2
>1/2-1/4k+(1/2-1/4k)^2/(k+1)^2
=1/2-1/4[k-(1/2-1/4k)^2/(k+1)^2]
=1/2-1/4[(k^3+2k^2+k-1+k-1/4k^2)/(k+1)^2]
>1/2-1/4[(k^3+3k^2+3k+1)/(k+1)^2]
=1/2-1/4[(k+1)^3/(k+1)^2]
=1/2-1/4(k+1)成立
所以an>1/2 -1/4n不太懂啊哪里不懂？先谢谢了。要求证的是“an>1/2 - 1/(4n)”呢，所以好像不对哦！