From ae2f16103529148f98857d17687079dd55e2db5d Mon Sep 17 00:00:00 2001 From: arc Date: Mon, 13 Oct 2025 14:57:06 -0600 Subject: [PATCH] vault backup: 2025-10-13 14:57:06 --- education/math/MATH1220 (calc II)/Sequences.md | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index 34d11fe..6138aed 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/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. \ No newline at end of file +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. \ No newline at end of file