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education/math/MATH1220 (calc II)/Sequences.md
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@@ -121,4 +121,4 @@ 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 $|R_N| \le a_{N+1}$.
So to determine the given error for any number of the series,
The error for the first $n$ terms of a sequence is less than or equal to the $(n + 1)$ st term of the sequence.