Abstract: The solution of sequence limits is the foundation of limit learning. This article explores the application of the definition of sequence limits, sequence limit operation techniques and Stolz theorem to solve sequence limits. During the process of solving sequence limits, two propositions are obtained, and the proof and application of propositions are explored. It is found that propositions can solve some problems in solving sequence limits. Finally, several methods for solving sequence limits are cited, providing reference for learning to solve sequence limits.

Key words: sequence limit, solution limit, Stolz theorem, substitution method