arc/notes
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

vault backup: 2025-10-13 14:57:06

Browse Source
This commit is contained in:
arc
2025-10-13 14:57:06 -06:00
parent e1be564bff
commit ae2f161035
1 changed files with 6 additions and 1 deletions
Download Patch File Download Diff File Expand all files Collapse all files

5
education/math/MATH1220 (calc II)/Sequences.md
View File

@@ -122,3 +122,8 @@ All three conditions hold true, therefore we know that $\sum_{n=1}^\infty \frac{
Let $\sum_{n=1}^\infty (-1)^n a_n$ be a series shown to converge by the alternating series test, and that it converges to a $L$. Then the remainder for a given term $N$ is $R_N = L - S_N$ . So $|R_N| \le a_{N+1}$. Let $\sum_{n=1}^\infty (-1)^n a_n$ be a series shown to converge by the alternating series test, and that it converges to a $L$. Then the remainder for a given term $N$ is $R_N = L - S_N$ . So $|R_N| \le a_{N+1}$.
The error for the first $n$ terms of a sequence is less than or equal to the $(n + 1)$ st term of the sequence. The error for the first $n$ terms of a sequence is less than or equal to the $(n + 1)$ st term of the sequence.
# Power Series
A power series centered at $c$ is a series of the form:
$$ \sum_{n=0}^\infty a_n(x-c)^n = a_0 + a_1(x-c) + a_2(x-c)^2 + \cdots$$
where $x$ is a variable.