The aim of this study is to investigate the concept knowledge about the limits of sequences of mathematics teacher candidates. Research is a case study in which qualitative methods are adopted. The first phase of the study was conducted with a total of 45 teacher candidates taking the course of Analysis III. At this stage, the "Limit Knowledge Test in Sequences", which was developed by the researchers to investigate the concept knowledge of the sequence concept, was used as a data collection tool. At this stage, "Limit Knowledge Test in Sequences", which was developed by researchers to investigate the limit concept knowledge in sequences of the teacher candidates, included 2 open-ended problems were used as data collection tool. In the second phase of the research, individual interviews were made with 8 teacher candidates selected from the sample to conduct in-depth research. Content analysis was used to analyze the obtained data. As a result of the analysis of the data, significant shortcomings were found in the knowledge of the concept of the limit topic in the sequences of teacher candidates. It is seen that the candidates do not know the importance of the concept of "accumulation point", which is indispensable to convergence.