题目内容
(本小题满分12分)已知函数
，数列
满足条件：
．
(1)求证：数列
为等比数列；
(2)令
是数列
的前
项和，求使
成立的最小的值．
【答案】
解：(1) 证明：由题意得
，∴ 
························· 3分
又 ∵ 
∴ 
················································································ 4分
故数列{bn + 1}是以1为首项，2为公比的等比数列·············································· 5分
(2) 由 (1) 可知，
，∴ 
·········································· 7分
故
················································ 9分
∴ 
············································ 10分
由
，且
，解得满足条件的最小值为10········································· 12分
【解析】略
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