Категория:Задачник Кузнецова Ряды Задача 14

В этой категории варианты Задачи 14, раздела "Ряды" в задачнике Кузнецова Л.А.

Варианты[править]

• в задачниках 2005 (красные) задача 10

Найти область сходимости функционального ряда.

Задача	Условие	Задача	Условие
14-1	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(n-2)^{3}(x+3)^{2n}}{2n+3}}}$	14-2	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(-1)^{n}(x-3)^{n}}{(n+1)5^{n}}}}$
14-3	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(x-1)^{2n}}{n\cdot 9^{n}}}}$	14-4	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {2n+3}{(n+1)^{5}x^{2n}}}}$
14-5	${\displaystyle \sum \limits _{n=1}^{\infty }(-1)^{n-1}{\frac {(x-2)^{2n}}{2n}}}$	14-6	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(x-5)^{2n+1}}{3n+8}}}$
14-7	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {n^{3}+1}{3^{n}(x-2)^{n}}}}$	14-8	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {n!}{x^{n}}}}$
14-9	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(x+5)^{2n-1}}{4^{n}(2n-1)}}}$	14-10	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(x-7)^{2n-1}}{\left(2n^{2}-5n\right)4^{n}}}}$
14-11	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(x-2)^{n}}{(3n+1)2^{n}}}}$	14-12	${\displaystyle \sum \limits _{n=2}^{\infty }{\frac {3n(x-2)^{3n}}{(5n-8)^{3}}}}$
14-13	${\displaystyle \sum \limits _{n=1}^{\infty }(x+5)^{n}\operatorname {tg} {\frac {1}{3^{n}}}}$	14-14	${\displaystyle \sum \limits _{n=1}^{\infty }\sin {\frac {\sqrt {n}}{n^{2}+1}}\cdot (x-2)^{n}}$
14-15	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {1}{n\cdot 9^{n}(x-1)^{2n}}}}$	14-16	${\displaystyle \sum \limits _{n=1}^{\infty }3^{n^{2}}x^{n^{2}}}$
14-17	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(x+2)^{n^{2}}}{n^{n}}}}$	14-18	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {n^{5}}{(n+1)!}}(x+5)^{2n+1}}$
14-19	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(3n-2)(x-3)^{n}}{(n+1)^{2}2^{n+1}}}}$	14-20	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(x-5)^{n}}{(n+4)\ln {(n+4)}}}}$
14-21	${\displaystyle \sum \limits _{n=2}^{\infty }{\frac {1}{(n+2)\ln {(n+2)}(x-3)^{2n}}}}$	14-22	${\displaystyle \sum \limits _{n=5}^{\infty }{\frac {1}{2^{n}n^{2}(x+2)^{n}}}}$
14-23	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(x-4)^{n^{2}}}{n^{n+1}}}}$	14-24	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {n^{5}}{x^{n}}}}$
14-25	${\displaystyle \sum \limits _{n=5}^{\infty }{\frac {\sqrt {n+1}}{3^{n}(x+3)^{n}}}}$	14-26	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {4^{n}(x+1)^{2n}}{n}}}$
14-27	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {3n+5}{(2n+9)^{5}(x+2)^{2n}}}}$	14-28	${\displaystyle \sum \limits _{n=5}^{\infty }{\frac {n^{2}+1}{5^{n}(x+4)^{n}}}}$
14-29	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(x+2)^{n}}{(2n+1)3^{n}}}}$	14-30	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {n^{2}(x-3)^{n}}{\left(n^{4}+1\right)^{2}}}}$
14-31	${\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(n+1)^{5}x^{2n}}{2n+1}}}$