Forgot password
 Register account
View 1148|Reply 2

无穷级数

[Copy link]

46

Threads

82

Posts

1

Reputation

Show all posts

Shiki posted 2019-7-20 21:48 |Read mode
Last edited by Shiki 2019-7-20 21:58$$\sum_{k=1}^{\infty}\frac {k}{k^4+4}=?$$
怎么拿这个考高中生呐。。。除了收敛什么都看不出来啊。。。


编辑:貌似可以裂项。。?

Related collections:

= =

673

Threads

110K

Posts

218

Reputation

Show all posts

kuing posted 2019-7-20 22:09
裂项就是由 `k^4+4=(k^2+2)^2-4k^2=\bigl((k-1)^2+1\bigr)\bigl((k+1)^2+1\bigr)` 得
\[\frac k{k^4+4}=\frac14\left(\frac1{(k-1)^2+1}-\frac1{(k+1)^2+1}\right)\]

673

Threads

110K

Posts

218

Reputation

Show all posts

kuing posted 2019-7-20 22:11

Quick Reply

Advanced Mode
B Color Image Link Quote Code Smilies
You have to log in before you can reply Login | Register account

$\LaTeX$ formula tutorial

Mobile version

2025-7-20 08:01 GMT+8

Powered by Discuz!

Processed in 0.015550 seconds, 25 queries