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...

问题详情：

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＜

【回答】

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＜.

*:B

知识点：数列

题型：选择题