问题标题:
已知数列{an}满足:a1=1,an+1=an+1n为奇数2ann为偶数(n∈N*),设bn=a2n-1.(I)求b2,b3,并证明:bn+1=2bn+2;(II)①证明:数列{bn+2}为等比数列;②若a2k,a2k+1,9+a2k+2成等比数列,求正整数k的值
问题描述:

已知数列{an}满足:a1=1,an+1=

an+1n为奇数2ann为偶数(n∈N*),设bn=a2n-1.

(I)求b2,b3,并证明:bn+1=2bn+2;

(II)①证明:数列{bn+2}为等比数列;②若a2k,a2k+1,9+a2k+2成等比数列,求正整数k的值.

齐世举回答:
  (I)∵数列{an}满足:a1=1,a
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