等差数列｛an｝,｛bn｝的前n项分别为Sn,Tn,若Sn/Tn=2n/3n+1,则an/bn=多少?

∵{an}与{bn}是等差数列∴Sn=[n(a1+an)]/2Tn=[n(b1+bn)]/2∴Sn/Tn=(a1+an)/(b1+bn)∵等差数列{an}与{bn}的前n项和的比为2n:(3n+1)∴(a1+an)/(b1+bn)=2n:(3n+1)假设(n+1)/2 =k {(n+1)/2为项数}则n=2k-1则ak/bk = 2(2k-1)/[3(2k-1)+1]=(2k-1)/(3k-1)即an/bn =(2n-1)/(3n-1) 回复：jiapeng12358当然不一定为整数只是替代法而已