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

@@ -94,3 +94,7 @@ Sometimes a series is not continually positive for the entire series, meaning mo
 
 A simple example of an alternating series is:
 $$ \sum_{n=1}^\infty (-1)^{n+1}a_n = a_1 - a_2 + a_3 - a_4 $$
+The above series converges if all three of the following hold true:
+- $a_n > 0$
+- Series decreases: $a_n \ge a_{n+1}$  for all $n$
+- $\lim_{n\to\infty} a_n = 0$ as_