vault backup: 2025-10-06 12:44:06

.obsidian/plugins/obsidian-git/data.json

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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,