题目

India has a very vast history and heritage（遗产）. The country has witnessed some of the most important events in the past and every event has an effect of its own on the culture, religion, lifestyle, and economy of the country. This is one of the leading reasons why tourists prefer India to travel and explore. Historical tours in India provide everything that a traveler expects from his/her journey. These historical tours give an opportunity to study and explore Indian history. Historical tours of India generally consisted of four phases: ancient, medieval（中世纪的）, moder已知数列{an}的前n项和为Sn，a2=，2Sn+1=3Sn+2（n∈N*）．（1）证明数列{an}为等比数列，并求出通项公式；（2）设数列{bn}的通项bn=，求数列{bn}的前n项的和Tn；（3）求满足不等式3Tn＞Sn（n∈N+）的n的值．