Question

设等比数列{ an}的公比为q,q>0且q≠1,Sn为{an}的前n项和,记Tn=an/Sn,则

Answer 1

a3=a1*q^2,a6=a1*q^5,S3=a1(1-q^3)/(1-q),S6=a1(1-q^6)/(1-q),

T3/T6=a3S6/a6S3=(1-q^6)/[(1-q^3)*q^3]=(1+q^3)(1-q^3)/[q^3(1-q^3)]

=(1+q^3)/q^3=1+q^(-3)>1

q>0 -> Tn=an/Sn>0 -> T3>T6