Finding finite sums, products and limits of some numerical sequences. Part 1. Application of methods of elementary mathematics and basic concepts of the theory of limits of numerical sequences

Authors

  • Valerii O. Bilyi Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • Oleksandr G. Bilyi Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine

DOI:

https://doi.org/10.20535/mmtu-2019.2-061

Keywords:

Finite sum, Finite product, Limit of numerical sequence, Mathematical induction, Recurrent relation

Abstract

When calculating the boundaries of numerical sequences and solving other problems of elementary and higher mathematics, there is a problem of calculating the sums and products of a finite number of numbers. The article considers some elementary methods of transformations ofsuch sums and products, in particular: reduction to arithmetic or geometric progression, method of mathematical induction, method of reduction of intermediate terms or coefficients, reduction of products, reduction to already known sums and products.

References

Alekseyev, V. M. (Ed.). (1977). Selected problems from the journal “American Mathematical Monthly” [in Russian]. Moscow: Mir.

Demidovich, B. P. (Ed.). (1970).Problems in mathematical analysis. Moscow: Mir Publishers.

Lyashko, I. I., Boyarchuk, A. K., Gai, Y. G., & Kalayda, A. F. (1983). Mathematical analysis: Textbook [in Russian] (Vol. 1). Kiev: Vyshcha Shkola.

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Issue

Vol. 2019 No. 2

Section

Methods of teaching and history of mathematics

License

Copyright (c) 2019 Mathematics in Modern Technical University

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