题目

Ren Yueli used to be a street singer at a subway station in Xidan Beijing. In 2008 she became popular online because she sang the song Angle's Wings beautifully. 【1】 .More recently, Ren became famous again. 【2】 .Su Qin, a famous writer, said on her Weibo that Ren's business had brought millions of yuan【3】 .However, Ren said in an interview. “【4】” She also said that the business idea came from a friend of hers. The friend is now working with her in the same factory. Compared with her singing career, her business is developing better.【5】 When someone asked her about the f（本小题满分14分）设数列的前项和为，对任意的正整数，都有成立，记。（I）求数列的通项公式；（II）记，设数列的前项和为，求证：对任意正整数都有；（III）设数列的前项和为。已知正实数满足：对任意正整数恒成立，求的最小值。