Abstract:The limit theory is one important part of higher mathematics. The limit of sequence, as one type of the core limits, is not only the forerunner of the limit theory, but also plays an important role in the field of economics and mathematics. The determination of the limit of sequence, as one important part of limit problem, is complex and diverse in its approaches, and closely related to the ways of expression of a sequence. After the study of the sequence defined by recursion formula, the method for calculating its limit is obtained.