设数列{an},{bn}都是正项等比数列,Sn,Tn分别为数列{lgan}与{lgbn}且Sn/Tn=n/2n+1,则lga5/lgb5=?

数列{an},{bn}都是正项等比数列,通项分别为q^(n-1),p^(n-1),则数列{lgan}与{lgbn}通项为(n-1)lgq和(n-1)lgp是等差数列,Sn=(n-1)²/2*lgq,Tn=(n-1)²/2*lgp,Sn/Tn=lgq/lgp=n/2n+1,则lga5/lgb5=5/11sorry啊，答案是9/19，麻烦您能再算一遍，可以吗？数列{an},{bn}都是正项等比数列,通项分别为a1*q^(n-1),b1*p^(n-1),则数列{lgan}与{lgbn}通项为lga1+(n-1)lgq和lgb1+(n-1)lgp是等差数列，公差分别为lgq和lgp，Sn=nlga1+n(n-1)lgq/2，Tn=nlgb1+n(n-1)lgp/2，Sn/Tn=[lga1+(n-1)lgq/2]/[lgb1+(n-1)lgp/2]=n/2n+1，lga5/lgb5=(lga1+4lgq)/(lgb1+4lgp),Sn/Tn=[lga1+(n-1)lgq/2]/[lgb1+(n-1)lgp/2]=n/2n+1当(n-1)/2=4时，即n=9，则Sn/Tn=(lga1+4lgq)/(lgb1+4lgp)=n/2n+1=9/19