...满足 , ,数列 的前 项和为 .(1)求数列 的通项公式;(2)设
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发布时间：2024-02-13 15:52
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时间：2024-03-06 11:25
整理得 ，----------------------------------------------------------------1分
∵ 否则 ，与 矛盾
从而得 , ---------------------------------------------------------------------3分
∵ ∴数列 是首项为1，公差为1的等差数列
∴ ，即 ．---------------------------------------------------------------4分
（2）∵
∴ ＝
＝ ---------------------------------------------------------6分
证法1：∵
＝ ＝
∴0 ．--------------------------------------------------------------------------8分
证法2：∵ ∴
∴
∴0 ．----------------------------------------------------------------------------8分
（3）用数学归纳法证明：
①当 时 ，不等式成立；-----------9分
②假设当 （ ， ）时，不等式成立，即
，那么当 时
----------------------------------------------------------------------12分
＝
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