由y=x^2-x+n/x^2+1得(y-1)x^2+x+y-n=0判别式大于或等于0,即1-4(y-1)(y-n)>=0,4y^2-4(n+1)y+4n-1=0[n+1-根号(n^2-2n+2)]/2<=y<=[n+1+根号(n^2-2n+2)]/2an=[n+1-根号(n^2-2n+2)]/2,bn=[n+1+根号(n^2-2n+2)]/2cn=4(an*bn-1/2)=4n- 展开
由y=x^2-x+n/x^2+1得(y-1)x^2+x+y-n=0判别式大于或等于0,即1-4(y-1)(y-n)>=0,4y^2-4(n+1)y+4n-1=0[n+1-根号(n^2-2n+2)]/2<=y<=[n+1+根号(n^2-2n+2)]/2an=[n+1-根号(n^2-2n+2)]/2,bn=[n+1+根号(n^2-2n+2)]/2cn=4(an*bn-1/2)=4n-3,Sn=n(2n-1)dn=Sn/(n+c)=n(2n-1)/(n+c),数列{dn}是等差数列,c=-1/2,dn=2nf(n)=Dn/(n+36)D(n+1)=2n/[(n+36)(2n+2)]=n/(n+36)(n+1)=1/[n+36/n+37]<=1/49(n=6时取等号).数列{f(n)}的最大项为1/49. 收起
