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级数前几项和s
n
=a
1
+a
2
+…+a
n
,若a
n
≥0,判断数列{s
n
}有界是级数
https://assets.asklib.com/psource/2015102616213461326.jpg
a
n
收敛的什么条件()?
A . 充分条件,但非必要条件
B . 必要条件,但非充分条件
C . 充分必要条件
D . 既非充分条件,又非必要条件
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设
https://assets.asklib.com/psource/2015103008504115623.jpg
,下列级数中绝对收敛的是()。
A .https://assets.asklib.com/psource/2015103008505988249.jpg
B .https://assets.asklib.com/psource/20151030085113680.jpg
C .https://assets.asklib.com/psource/2015103008512720453.jpg
D .https://assets.asklib.com/psource/2015103008514346537.jpg
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下列级数中,条件收敛的级数是().
A .https://assets.asklib.com/psource/2015102915252363975.jpg
B .https://assets.asklib.com/psource/2015102915253710012.jpg
C .https://assets.asklib.com/psource/2015102915254926048.jpg
D .https://assets.asklib.com/psource/2015102915260616375.jpg
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级数是条件收敛还是绝对收敛?afb2c17958631f06f3b5821f70316926.pngc451fac0d0b3be5a84e1f28be9f37a4e.png
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设级数绝对收敛,则级数( )
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设,则收敛半径R=(),故幂级数在()绝对收敛,在()一致收敛。
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。
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设(n=3,4,5.....),证明: (1)级数绝对收敛; (2)数列{a<sub>n</sub>}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<sub>n</sub>}收敛.
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设幂级数 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
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设 为收敛的正项级数,证明 绝对收敛.
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.
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若级数收敛于S,则级数收敛于______
若级数<img src='https://img2.soutiyun.com/ask/2019-12-28/946403212628433.png' />收敛于S,则级数<img src='https://img2.soutiyun.com/ask/2019-12-28/946403223216556.png' />收敛于______
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判别下列级数的收敛性,若收敛,是绝对收敛还是条件收敛?
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若级数习绝对收敛,则级数习必定();若级数习条件收敛,则级数必定().
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().
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证明:若都绝对收敛,则级数也绝对收敛。
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。
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证明:级数在[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: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.
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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/2020-12-14/976812927934874.png' />且<img src='https://img2.soutiyun.com/ask/2020-12-14/976812935497307.png' />收敛,则对于任意正数p,级数<img src='https://img2.soutiyun.com/ask/2020-12-14/976812944562825.png' />().
A.绝对收敛
B.条件收敛
C.发散
D.敛散性与p有关
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讨论反常积分λ取何值时绝对收敛或条件收敛.
讨论反常积分<img src='https://img2.soutiyun.com/ask/2020-11-30/975594851517965.png' />λ取何值时绝对收敛或条件收敛.
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29、绝对收敛的级数一定收敛.
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若绝对收敛,证明下列级数也绝对收敛:
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' />
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判断下列复级数的敛散性,若收敛指明条件收敛还是绝对收敛. 设D是一个有界区域,其边界为aD,若fn()+… 在 上一致收敛.
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级数<img src='http://221.174.24.96:6088/latex/latex.action?latex=xhn1bv97bj0xfv57k1xpbmz0ex0oltepxntufvxmcmfjezj9e259' />是否收敛?若收敛,是条件收敛还是绝对收敛?
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已知级数收敛,证明绝对收敛。
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。
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证明:若级数绝对收敛,则函数项级数在R一致收敛.
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.
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幂级数在()绝对收敛,在()发散。
幂级数<img src='https://img2.soutiyun.com/ask/2020-12-14/976814121928167.jpg' />在()绝对收敛,在()发散。
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将函数f(x)=x(x-π)展开成以2π为周期的傅里叶级数,并回答:(I)级数在点x=±π和x=2π分别收敛于何值
将函数f(x)=x(x-π)展开成以2π为周期的傅里叶级数,并回答:
(I)级数在点x=±π和x=2π分别收敛于何值?(II)<img src='https://img2.soutiyun.com/ask/2021-01-11/979241771846486.png' />