求幂级数 的收敛域及和函数./ananas/latex/p/617279

A . （-1，1） B . （-1，1） C . （3，7） D . （4，5）

A . 0B . πC .https://assets.asklib.com/images/image2/2017051111193844963.jpg D .https://assets.asklib.com/images/image2/2017051111194477734.jpg

A .https://assets.asklib.com/psource/201510291530231830.jpg B .https://assets.asklib.com/psource/2015102915303768116.jpg C .https://assets.asklib.com/psource/2015102915305046680.jpg D .https://assets.asklib.com/psource/2015102915310234816.jpg

A:symsum; B:taylor; C:taylortool; D:sym2poly

<img src='https://img2.soutiyun.com/ask/2019-04-23/92487125804009.png' />

<img src='https://img2.soutiyun.com/ask/2021-01-25/98044366648261.png' />

A．部分和数列有界 B．部分和数列极限为零 C D．都收敛

<img src='https://img2.soutiyun.com/ask/2020-12-10/976481945992252.png' />

<img src='https://img2.soutiyun.com/ask/2021-01-05/978723648645819.png' /> <img src='https://img2.soutiyun.com/ask/2021-01-05/978723658290371.png' />

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。

将函数<img src='https://img2.soutiyun.com/ask/2020-12-14/97678986011847.png' />展开成简单幂级数,并指出它收敛的区间.

求幂级数<img src='https://img2.soutiyun.com/ask/2020-12-11/976533602465549.png' />的收敛域及和函数,并求常数项级数<img src='https://img2.soutiyun.com/ask/2020-12-11/976533633968351.png' />的和.

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.

<img src='https://img2.soutiyun.com/ask/2020-12-22/977477173109151.png' />

<img src='https://img2.soutiyun.com/ask/2020-08-21/966869110386338.png' />

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' />