已知等比数列{an}中，a1>0，q>0，前n项和为Sn，比较S3a3与S5a5的大小结果为．

Question

已知等比数列{a_n}中，a₁>0，q>0，前n项和为S_n，比较(S3)/(a3)与(S5)/(a5)的大小结果为 ___．

Answer 1

当q=1时，(S3)/(a3)=3，(S5)/(a5)=5，所以(S3)/(a3)<(S5)/(a5)；当q>0且q≠1时，(S3)/(a3)-(S5)/(a5)=((a1(1-q3))/(1-q))/(a1q2)-((a1(1-q5))/(1-q))/(a1q4)=-(1+q)/(q4)<0，所以有(S3)/(a3)<(S5)/(a5)．
综上可知(S3)/(a3)<(S5)/(a5)．
故答案为：(S3)/(a3)<(S5)/(a5)．