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

@@ -142,4 +142,9 @@ The behavior a given power series falls into one of three cases:
 > When does the series $\sum_{n=0}^\infty \frac{x^n}{3^n}$ converge?
 1.  Solving for any power series usually starts with the ratio test.
 		1. Create a ratio with $n + 1$ and $n$. 
-		$$ \frac{x^{n+1}}{3^{n+1}} \cdot \frac{3^n}{x^n} $$
+		$$ \frac{x^{n+1}}{3^{n+1}} \cdot \frac{3^n}{x^n} $$
+		2. Cancel stuff out
+		$$ \frac{x}{3}$$
+2. For a geometric series, it converges when the ratio $r$ is less than one. Written as an equality, this gives us:
+$$ |r| < 1 \to |\frac{x}{3}| < 1 \to |x| < 3 $$
+This means that the interval of convergence is $(-3, 3)$