from 01.01.2004 to 01.01.2023
Kemerovo, Kemerovo, Russian Federation
Continuity is very important at the intersection of school and higher education. In particular, it concerns the continuity of mathematical analysis at school and university. The school course of basic mathematical analysis brings up mathematical culture and scientific outlook. It is crucial for higher education in physics, mathematics, and information technology. To structure the course of mathematical analysis and prevent possible difficulties, the university professor needs to actualize the existing knowledge and skills in first-year students by providing the continuity of theory and practice. The article describes the methodological approach to continuity for some mathematical formulas in the university course of mathematical analysis, i.e., the two-degree summation formulas of Newton’s binomial formula of reduced multiplication and the formula of the sum of infinitely decreasing geometric series. In algebra and mathematical analysis, these formulas are used to work with polynomials and analytic functions. These formulas and their generalized versions allow university students to use more rational and creative methods of mathematical analysis for calculating limits of sequences and functions. They provide a universal method that can be applied to problems of the theory of limits in the course of mathematical analysis at school and university. The case is an example of effective continuity of mathematical education in the school-university system.
continuity, mathematical analysis, Newton’s binomial, infinite geometric progression, Taylor-Maclaurin formula, limit of function
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