Training Manual . — Troitsk: Federal Agency for Education Troitskiy Branch of the State Educational Institution of Higher Professional Education "Chelyabinsk State University" Department of Mathematics and Informatics, 2010. — 51 s. The textbook is compiled on the basis of the discipline program "Mathematical Analysis" . The manual presents theoretical and practical material on the topic "Number rows", studied by students of the specialty "Applied mathematics and computer science" . The manual is distinguished by a summary brevity and simplicity of presentation . Can be used to conduct practical classes and organize independent work of students, as well as to prepare students for the state exam . The training manual is intended for teachers and students.. Number series theory . Basic definitions and simplest properties of numerical series. Rows with non-negative members. Common signs of series convergence. Reshuffle of members of a number of. Examples of problem solving and tasks for independent solution. The similarity of the numerical series, its sum, partial sums. Cauchy Convergence Criterion Series. The necessary condition for the convergence of the series. The simplest converging series and their properties. Weierstrass criterion for series with non-negative members. First and second signs of comparison. Signs of Cauchy and Dalumber . Other Sufficient Signs of Convergence. Rows with arbitrary members. Literature.