设等差数列{ an},{bn}前n项的各分别为Sn与Tn,若Sn/Tn=(2n)/(3n+1),则an/bn=?(要解题步骤)

设等差数列{ an},{bn}前n项的各分别为Sn与Tn,若Sn/Tn=(2n)/(3n+1),则an/bn=?(要解题步骤)
设等差数列{ an},{bn}前n项的各分别为Sn与Tn,若Sn/Tn=(2n)/(3n+1),则an/bn=?(要解题步骤)

设等差数列{ an},{bn}前n项的各分别为Sn与Tn,若Sn/Tn=(2n)/(3n+1),则an/bn=?(要解题步骤)
附图是详细解答

Sn/Tn=2n/(3n+1),即
S(2n-1)/T(2n-1)=2(2n-1)/[3(2n-1)+1]=(2n-1)/(3n-1),即
[a1+a（2n-1）]/[b1+b(2n-1)]=(2n-1)/(3n-1),即
2an/2bn=(2n-1)/(3n-1),
an/bn=(2n-1)/(3n-1)