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．
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
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