设，则收敛半径R=（)，故幂级数在（)绝对收敛，在（)一致收敛。

A . （-1，l] B . ［-1，1] C . ［-1，1） D . （-∞，+∞）

A . （-2，2） B . （-2，4） C . （0，4） D . （-4，0）

A . ｜x｜<2时 B . ｜x｜>1／4时 C . ｜x｜<4时 D . ｜x｜>1／2时

A . R=2B . R=1C .https://assets.asklib.com/images/image2/201705111629205302.jpg D .https://assets.asklib.com/images/image2/2017051116285725842.jpg

设幂级数<img src='https://img2.soutiyun.com/ask/2020-12-14/976788824298225.png' />的收敛半径为R,而<img src='https://img2.soutiyun.com/ask/2020-12-14/976788837697991.png' />的收敛半径为R,若把幂级数<img src='https://img2.soutiyun.com/ask/2020-12-14/976788854253938.png' />的收敛半径记为R,证明: (1)<img src='https://img2.soutiyun.com/ask/2020-12-14/976788868991781.png' />; (2)当R₁≠R₂时,<img src='https://img2.soutiyun.com/ask/2020-12-14/976788887921864.png' />.

设<img src='https://img2.soutiyun.com/ask/2020-12-17/977061005028657.png' />(n=3,4,5.....)，证明: (1)级数绝对收敛; (2)数列{a_n}收敛.

设幂级数<img src='https://img2.soutiyun.com/ask/2020-11-02/973183367447765.png' />处收敛,则此级数在x=2处() A.条件收敛 B.绝对收敛 C.发散 D.收敛性不能确定

设<img src='https://img2.soutiyun.com/ask/2020-11-02/973182947687756.png' />为收敛的正项级数,证明<img src='https://img2.soutiyun.com/ask/2020-11-02/973182957364309.png' />绝对收敛.

0； 1； 正无穷大； 不能确定。

5．设幂级数<img src='https://img2.soutiyun.com/latex/latex.action' />的收敛半径为R(0＜R＜+∞)，则当______时，该幂级数绝对收敛；当______时，该幂级数发散。

若级数习<img src='https://img2.soutiyun.com/ask/2020-11-26/975244241398906.png' />绝对收敛,则级数习<img src='https://img2.soutiyun.com/ask/2020-11-26/975244252374534.png' />必定();若级数习<img src='https://img2.soutiyun.com/ask/2020-11-26/97524427328373.png' />条件收敛,则级数<img src='https://img2.soutiyun.com/ask/2020-11-26/97524428376933.png' />必定().

证明：若<img src='https://img2.soutiyun.com/ask/2021-01-14/979479445751123.jpg' />都绝对收敛，则级数<img src='https://img2.soutiyun.com/ask/2021-01-14/979479456785754.jpg' />也绝对收敛。

A．1 B．3 C．<img src='https://img2.soutiyun.com/latex/latex.action' />D．∞

若<img src='https://img2.soutiyun.com/ask/2020-08-10/965908063220218.png' />,则幂级数<img src='https://img2.soutiyun.com/ask/2020-08-10/965908072452746.png' />的收敛半径是()。

对幂级数<img src='https://img2.soutiyun.com/ask/2020-11-03/973272201073886.png' />,记<img src='https://img2.soutiyun.com/ask/2020-11-03/973272214906677.png' />,则 <img src='https://img2.soutiyun.com/ask/2020-11-03/973272227464395.png' /> 那么,此幂级数的收敛半径是<img src='https://img2.soutiyun.com/ask/2020-11-03/973272239670093.png' />还是6？

证明如果<img src='https://img2.soutiyun.com/ask/2021-03-11/984303389062117.png' />存在(≠∞)，则下列三个幂级数有相同的收敛半径： <img src='https://img2.soutiyun.com/ask/2021-03-11/984303456387967.png' />

证明:若级数<img src='https://img2.soutiyun.com/ask/2020-11-13/974117042967238.jpg' />绝对收敛,则函数项级数 <img src='https://img2.soutiyun.com/ask/2020-11-13/974117058462124.png' /> 在R一致收敛.

若幂级数<img src='https://img2.soutiyun.com/ask/2020-08-10/965908113007065.png' />的收敛半径分别是R₁和R₂，则R₁和R₂的大小关系是()。