已知函数.数列.满足条件:．(1)求证:数列为等比数列,(2)令.Tn是数列的前n项和.求

发布时间：2021-02-21 07:52:45

(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，Tn是数列的前n项和，求使成立的最小的n值．


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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，得
∴满足条件的n的最小值为10···································································· 12分

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