From 0123762cee6f34bf9588fd19305c2033be371ea5 Mon Sep 17 00:00:00 2001
From: arc <zleyyij@users.noreply.github.com>
Date: Mon, 6 Oct 2025 12:44:06 -0600
Subject: [PATCH] vault backup: 2025-10-06 12:44:06

---
 .obsidian/plugins/obsidian-git/data.json      | 27 +++++++++++++++++++
 .../math/MATH1220 (calc II)/Sequences.md      |  4 +++
 2 files changed, 31 insertions(+)

diff --git a/.obsidian/plugins/obsidian-git/data.json b/.obsidian/plugins/obsidian-git/data.json
index e69de29..4bc189e 100644
--- a/.obsidian/plugins/obsidian-git/data.json
+++ b/.obsidian/plugins/obsidian-git/data.json
@@ -0,0 +1,27 @@
+{
+  "commitMessage": "vault backup: {{date}}",
+  "autoCommitMessage": "vault backup: {{date}}",
+  "commitDateFormat": "YYYY-MM-DD HH:mm:ss",
+  "autoSaveInterval": 5,
+  "autoPushInterval": 0,
+  "autoPullInterval": 5,
+  "autoPullOnBoot": false,
+  "disablePush": false,
+  "pullBeforePush": true,
+  "disablePopups": false,
+  "listChangedFilesInMessageBody": false,
+  "showStatusBar": true,
+  "updateSubmodules": false,
+  "syncMethod": "merge",
+  "customMessageOnAutoBackup": false,
+  "autoBackupAfterFileChange": false,
+  "treeStructure": false,
+  "refreshSourceControl": true,
+  "basePath": "",
+  "differentIntervalCommitAndPush": false,
+  "changedFilesInStatusBar": false,
+  "showedMobileNotice": true,
+  "refreshSourceControlTimer": 7000,
+  "showBranchStatusBar": true,
+  "setLastSaveToLastCommit": false
+}
\ No newline at end of file
diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md
index e1bc0d3..c61dc78 100644
--- a/education/math/MATH1220 (calc II)/Sequences.md	
+++ b/education/math/MATH1220 (calc II)/Sequences.md	
@@ -118,3 +118,7 @@ Then if the *series converges* absolutely then the sum converges.
 	- $\lim_{n \to \infty} a_n = 0$ - the series approaches zero
 All three conditions hold true, therefore we know that $\sum_{n=1}^\infty \frac{(-1)^n}{n+5}$ conditionally converges.
 
+## 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 $|R_N| \le a_{N+1}$. 
+
+So to determine the given error for any number of the series, 
\ No newline at end of file