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

education/math/MATH1220 (calc II)/Sequences.md

@@ -121,4 +121,9 @@ All three conditions hold true, therefore we know that $\sum_{n=1}^\infty \frac{
 ## Error
 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.