y已知F(X)=3X^2-2X,数列AN的前N项和为SN,点（N,SN)均在函数y=f（x）y已知F(X)=3X^2-2X,数列AN的前N项和为SN,点（N,SN)均在函数y=f（x）上,求AN BN=1/AN*A(N+1)使BN前N项和Tn,求使得TN

y已知F(X)=3X^2-2X,数列AN的前N项和为SN,点（N,SN)均在函数y=f（x）y已知F(X)=3X^2-2X,数列AN的前N项和为SN,点（N,SN)均在函数y=f（x）上,求AN BN=1/AN*A(N+1)使BN前N项和Tn,求使得TN
y已知F(X)=3X^2-2X,数列AN的前N项和为SN,点（N,SN)均在函数y=f（x）
y已知F(X)=3X^2-2X,数列AN的前N项和为SN,点（N,SN)均在函数y=f（x）上,求AN BN=1/AN*A(N+1)使BN前N项和Tn,求使得TN

y已知F(X)=3X^2-2X,数列AN的前N项和为SN,点（N,SN)均在函数y=f（x）y已知F(X)=3X^2-2X,数列AN的前N项和为SN,点（N,SN)均在函数y=f（x）上,求AN BN=1/AN*A(N+1)使BN前N项和Tn,求使得TN
x=n f(x)=Sn代入函数方程：
Sn=3n²-2n
n=1时,S1=a1=3-2=1
n≥2时,Sn=3n²-2n S(n-1)=3(n-1)²-2(n-1)
an=Sn-S(n-1)=3n²-2n-3(n-1)²+2(n-1)=6n-5
n=1时,a1=6-5=1,同样满足.
数列{an}的通项公式为an=6n-5.
bn=1/[ana(n+1)]=1/[(6n-5)(6n+1)]=(1/6)[1/(6n-5)-1/(6n+1)]
Tn=b1+b2+...+bn
=(1/6)[1/1-1/7+1/7-1/13+.+1/(6n-5)-1/(6n+1)]
=(1/6)[1-1/(6n+1)]
=n/(6n+1)
Tn+∞时,10/[3(6n+1)]>0且->0,(10/3)-10/[3(6n+1)]10/3
要不等式对于所有正整数n恒成立,则m≥10/3,又m为正整数m≥4
满足不等式恒成立的最小正整数m是4.