In fact, only you can understand this kind of thing. Of course, some important inequalities must be mastered very skillfully. The proof of Cauchy inequality must be successful, and it may appear in the proof of ordinary inequality. If it is generally proved that the inequality of a sequence allows you to find that the sum of the sequence is less than a certain number, then it can be proved by the boundedness of the sequence, which is the popular limit (convergence) of the sequence. In our teacher's words, a common method to find the limit is to use "L'H?pital's Law", which is not taught in senior high school. The method is that for functions of 0/0 type and infinite/infinite type, the upper and lower derivatives can be taken respectively, and then the limit can be found. Take a look at Baidu specifically! I hope it helps you.