eng Science and Education Publishing American Journal of Educational Research 2327-6150 2015-12-19 3 12B 16 19 10.12691/education-3-12B-4 EDUCATION2015312B4 article Bosovskyi Mykola 1 Bochko Oksana ok.volovik@gmail.com 1 Tretyak Mykola 1 Bohdan Khmelnytskyy National University of Cherkasy, Cherkasy, Ukraine The article describes methods of studying the limits of sequences and theorems of the limits of the sequences. Aspects of studying the limits of the sequence, an offered roll-out of "Limit of the sequence" theme and the study of the basic theorems on the limits of sum, product and quotient of two sequences have been developed. Theoretical generalization has been performed and a new approach in the introduction and study of uncertainties as statements that complement the theorems has been suggested. http://pubs.sciepub.com/education/3/12B/4/education-3-12B-4.pdf methods of teaching mathematics mathematical analysis theory of limits institute of higher education theoretical analysis limit of the sequence limit of the quotient limit of the sum limit of the product mathematical phrases uncertainties