Keyword: «necessary and sufficient conditions of convergence»

In order to increase the level of mathematical preparation of students of mathematical and technical specialties special attention is paid to the issues of higher mathematics, without a solid knowledge of which it is impossible to become good specialists in their field. Such important topics include the topic of numerical series. Their use is very wide: approximate evaluation of functions and integrals, replacement of complex functions is more straightforward, in particular by polynomials, whose properties are well studied; calculation of the limits, solution of differential equations. The paper deals with the example task to demonstrate the technique of the study of the convergence of numerical series with positive terms and benefits of this technique. The material is designed for students of technical specialties, but will be useful to the one interested in the theory of series. The author presents recommendations in the form of tasks and examples for exam preparation, practical training, control and watershed work, homework. The work material can be used by teachers, leading practical classes. The author assumes that the reader knows the basic concepts of the theory of infinitely small and large quantities, their comparison, different ways of calculating the limits.