设且收敛,则对于任意正数p,级数（).A.绝对收敛B.条件收敛C.发散D.敛散性与p有关

设<img src='https://img2.soutiyun.com/ask/2020-12-14/976814132759786.jpg' />，则收敛半径R=()，故幂级数<img src='https://img2.soutiyun.com/ask/2020-12-14/976814148615693.jpg' />在()绝对收敛，在()一致收敛。

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.

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。

证明:级数<img src='https://img2.soutiyun.com/ask/2021-01-05/97872007433638.png' />在[0,1]上绝对并一致收敛,但由其各项绝对值组成的级数在[0,1]上却不一致收敛.

证明函数项级数<img src='https://img2.soutiyun.com/ask/2021-01-28/980691494484278.png' />上是一致收敛的，其中a是小于<img src='https://img2.soutiyun.com/ask/2021-01-28/980691504747866.png' />的任意固定正数。

对于级数习<img src='https://img2.soutiyun.com/ask/2020-12-07/976201851181314.png' />下列结论中正确的是(). A.a＞1时,级数收敛 B.a＜1时,级数发散 C.a=1时,级数收敛 D.a=1时,级数发散

若<img src='https://img2.soutiyun.com/ask/2020-12-14/976827987925256.png' />绝对收敛，证明下列级数也绝对收敛: <img src='https://img2.soutiyun.com/ask/2020-12-14/976827980220816.png' />

已知级数<img src='https://img2.soutiyun.com/ask/2021-01-20/9799846556874.png' />收敛，证明<img src='https://img2.soutiyun.com/ask/2021-01-20/979984676783606.png' />绝对收敛。

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.