(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．

题型：不详难度：来源：

(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{b_n+ 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