數列{an}中,an＞0,且{anan+1}是公比爲q(q＞0)的等比數列,滿足anan+1+an+1an+2...

問題詳情：

數列{an}中,an＞0,且{anan+1}是公比爲q(q＞0)的等比數列,滿足anan+1+an+1an+2＞an+2an+3(n∈N*),則公比q的取值範圍是(    )

A.0＜q＜                                        B.0＜q＜

C.0＜q＜                                      D.0＜q＜

【回答】

解析:∵{anan+1}的公比爲q,

∴an+1an+2＝qanan+1,an+2an+3＝q2anan+1.

∵an＞0,∴q＞0且1+q＞q2,

解得0＜q＜.

*:B

知識點：數列

題型：選擇題