Ряды
книга

Ряды

Автор: Анна Ядута

Форматы: PDF

Издательство: Директ-Медиа

Год: 2021

Место издания: Москва|Берлин

ISBN: 978-5-4499-2521-3

Страниц: 148

Артикул: 90648

Возрастная маркировка: 12+

Печатная книга
791
Ожидаемая дата отгрузки печатного
экземпляра: 11.04.2024
Электронная книга
207.2

Краткая аннотация книги "Ряды"

Данное пособие составлено в соответствии с программой «Высшая математика» для технических вузов и предназначено для студентов всех специальностей и всех форм обучения.
This handbook is made in accordance with the program «Higher mathematics» for technical universities and is intended for students of all majors and all forms of learning.

Содержание книги "Ряды"


Introduction
§1. Series with positive terms. Necessary tests for convergence and comparison tests of series with positive terms
Examples to §1
Individual exercises for §1
§2. Sufficient Tests for Convergence of positive numerical series
Examples to § 2
Individual exercises for § 2
§ 3. Alternating series. Leibniz and Cauchy theorems
Examples to § 3
Individual exercises for § 3
§ 4. Functional series. study of convergence and uniform convergence of functional series
Examples to § 4
Individual exercises for к § 4
§ 5. Power series
Examples to § 5
Individual exercises for к § 5
§ 6. Expanding functions into power series
Examples to § 6
Individual exercises for § 6
§ 7. Application of series to approximate calculations
Examples to § 7
Individual exercises for к § 7
Individual home work IHW-1
Solutions to typical questions IHW №1
IHW-2
Solutions to typical questions IHW 2
Appendices
Factorial
Bibliography

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11111!1!1lim!!11limlimnnnnnnnnnnnnnnnnnuub 111lim1lim!1!1lim ennnnnnnnnnnnnnn. The series diverges. Example 35 [5]. Determine convergence of the series ...2...32221210103102nn. Solution. Applying d’Alembert’s ratio test; we have 102nunn, 101112nunn, 1010112nnuunn, meaning, 2112lim12lim101010nnnbnn. Such that1b, then the series diverges. Example 36 [5]. Determine convergence of the series ...395943333231. Solution. Here, 23nnnu, 21131nnnu, 311nnuunn; therefore 31311lim31limnnnbnn; 1b. Consequently, the series converges. Example 37 [5]. Determine convergence of the series ...!310!210!11032. Solution. We have !10nunn, !11011nunn, 1101nuunn. 0110limnbn; 1b – series converges. Example 38 [12]. Determine convergence of the series 1153nnnn. Solution. Applying Cauchy’s test. Such that 153153nnnnunnnn, 153153lim153limlimnnnunnnnn. 26