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2023•CURRENT PROBLEMS OF TEACHING MATHEMATICS AT TECHNICAL UNIVERSITYOpen access

ABOUT THE NECESSARY CONDITIONS AND SUFFICIENT CONDITIONS FOR CONVERGENCE OF A SEQUENCE

S. K. Sobolev, V. Ya. Tomashpolsky, A. O. Golosov

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Abstract

Methodological aspects of teaching the section "limit of sequence and function" in a technical university are discussed. The application of various necessary convergence conditions to justify the absence of a sequence limit is considered. The applications of sufficient conditions to justify convergence and to calculate the limit of the sequence are discussed. The methods of finding the limit of recurrent sequences converging to a fixed point are analyzed. The application of the Lipschitz condition, which guarantees the convergence of a recurrent sequence, is analyzed.

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Methodological aspects of teaching the section "limit of sequence and function" in a technical university are discussed. The application of various necessary convergence conditions to justify the absence of a sequence limit is considered. The applications of sufficient conditions to justify convergence and to calculate the limit of the sequence are discussed. The methods of finding the limit of recurrent sequences converging to a fixed point are analyzed. The application of the Lipschitz condition, which guarantees the convergence of a recurrent sequence, is analyzed.

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Available abstract

Methodological aspects of teaching the section "limit of sequence and function" in a technical university are discussed. The application of various necessary convergence conditions to justify the absence of a sequence limit is considered. The applications of sufficient conditions to justify convergence and to calculate the limit of the sequence are discussed. The methods of finding the limit of recurrent sequences converging to a fixed point are analyzed. The application of the Lipschitz condition, which guarantees the convergence of a recurrent sequence, is analyzed.

Key concepts: Sequence (biology), Limit (mathematics), Limit of a sequence, Convergence (economics), Lipschitz continuity, Limit point, Mathematics, Applied mathematics

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