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

@@ -130,4 +130,12 @@ where $x$ is a variable.
 
 $\sum x^n$ converges when $|x| < 1$  and diverges when $|x| \ge 1$. 
 
-The above series is a series of the 
+The above series is a power series where $a_n = 1$  and $c = 0$.
+
+## Behavior
+The behavior a given power series falls into one of three cases:
+1. The series converges on an interval with radius $R > 0$ When this happens, each interval endpoint needs to be checked independently, because the ratio test will always be indeterminate at those points.
+2. The series converges for all $x = \mathbb{R}$
+3. 
+
+# Examples