Trance-0/NoteNextra-origin
1
0
Fork 0
Code Issues Pull Requests Actions 1 Packages Projects Releases Wiki Activity

final update on 4121

Browse Source
This commit is contained in:
Trance-0
2025-05-04 19:38:10 -05:00
parent 9c93651852
commit 1a2ec73539
9 changed files with 804 additions and 29 deletions
Download Patch File Download Diff File Expand all files Collapse all files

4
pages/Math4121/Math4121_L13.md
View File

@@ -89,12 +89,16 @@ x-\lfloor x \rfloor & x \in [\lfloor x \rfloor, \lfloor x \rfloor + \frac{1}{2})
x-\lfloor x \rfloor - 1 & x \in (\lfloor x \rfloor + \frac{1}{2}, \lfloor x \rfloor + 1] \end{cases}
$$
![Graph of y=((x))](https://notenextra.trance-0.com/Math4121/y=((x)).png)
We define
$$
f(x) = \sum_{n=1}^{\infty} \frac{((nx))}{n^2}=\lim_{N\to\infty}\sum_{n=1}^{N} \frac{((nx))}{n^2}
$$
![Graph of y=f(x)](https://notenextra.trance-0.com/Math4121/sum_y=((x)).png)
(i) The series converges uniformly over $x\in[0,1]$.
$$