题目

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＜ 答案：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

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