等差数列{an}和{bn}的前n项和分解为Sn和Tn,且Sn/Tn=2n/(3n+1),则a5/b5=?

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等差数列{an}和{bn}的前n项和分解为Sn和Tn,且Sn/Tn=2n/(3n+1),则a5/b5=?等差数列{an}和{bn}的前n项和分解为Sn和Tn,且Sn/Tn=2n/(3n+1),则a5/

等差数列{an}和{bn}的前n项和分解为Sn和Tn,且Sn/Tn=2n/(3n+1),则a5/b5=?
等差数列{an}和{bn}的前n项和分解为Sn和Tn,且Sn/Tn=2n/(3n+1),则a5/b5=?

等差数列{an}和{bn}的前n项和分解为Sn和Tn,且Sn/Tn=2n/(3n+1),则a5/b5=?
用“首项加末项,乘以项数除以2”的那个前n项和公式,分别代入到已知等式中的Sn,Tn中很容易得到：[（a1+an)/2]/[(b1+bn)/2]=2n/(3n+1)
即（a1+an）/(b1+bn)=2n/(3n+1) （1）
而2a5=a1+a9
2b5=b1+b9
两式相除,再据（1）式就得：
a5/b5=(a1+a9)/(b1+b9)＝2*9/(3*9+1)=18/28=9/14

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