数列{an}中,an＞0,且{anan+1}是公比为q(q＞0)的等比数列,满足anan+1+an+1an+2＞an+2an+3(n∈N*),则公比q的取值范围是( )
A.0＜q＜
B.0＜q＜
C.0＜q＜
D.0＜q＜
数列{an}中,an＞0,且{anan+1}是公比为q(q＞0)的等比数列,满足anan+1+an+1an+2＞an+2an+3(n∈N*),则公比q的取值范围是( )
A.0＜q＜ B.0＜q＜
C.0＜q＜ D.0＜q＜
解析:∵{anan+1}的公比为q,
∴an+1an+2＝qanan+1,an+2an+3＝q2anan+1.
∵an＞0,∴q＞0且1+q＞q2,
解得0＜q＜.
答案:B