首项为a1,公比为q的等比数列前n项和为Sn,则数列{1/an}的前n项和Tn=-----

首项为a1,公比为q则an=a1*q^(n-1)所以1/a1+1/a2+1/a3+。+1/an=1/a1*[(1+1/q+1/q^2+。。。+1/q^(n-1)]=1/a1*[(1-1/q^n)/(1-1/q)]=1/a1[1/q^(n-1)]*(q^n-1)/(q-1)=Sn/q^(n-1)