Keyword: «necessary and sufficient signs of convergence»

The theme related to the study of numerical series for convergence is complex and important in the further study of mathematics. Therefore, it is necessary that students could easily and quickly find numerical series convergence signs. In this article on task examples the author presents the application method of Kummer sign from which originally followed well-known sufficient signs of numerical series with positive terms convergence study by d'Alembert, Cauchy, Raabe, Bertrand, Gauss and others. The article material is intended for students of technical specialties and it will be useful to all those who are interested in the theory of series. The article presents recommendations in the form of tasks and examples for exam preparation, practical training, control work and homework. The work material can be used by teachers conducting practical and theoretical classes. The article results from years of teaching experience and it is essentially a plan for practical classes on this subject. The author presumes that the reader possesses the skills of limits calculation, the basic concepts of infinitely small and large quantities theory and their comparison.