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

@@ -126,4 +126,8 @@ The error for the first $n$ terms of a sequence is less than or equal to the $(n
 # Power Series
 A power series centered at $c$ is a series of the form:
 $$ \sum_{n=0}^\infty a_n(x-c)^n = a_0 + a_1(x-c) + a_2(x-c)^2 + \cdots$$
-where $x$ is a variable.
+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