Question

设无穷等比数列{an}的前n项和为Sn,首项是a1,若limSn=a1^2,a1∈(1,4)

则公比q的取值范围是？

Answer 1

limSn=a1/(1-q)=a1^2 ①

|q|<1②
由①，得
a1=1/(1-q)
1<1/(1-q)<4
1>1-q>1/4
0>-q>-3/4
0<q<3/4
和②取交集，所以
0<q<3/4