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education/math/MATH1220 (calc II)/Sequences.md
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@@ -140,4 +140,6 @@ The behavior a given power series falls into one of three cases:
# Examples # Examples
> When does the series $\sum_{n=0}^\infty \frac{x^n}{3^n}$ converge? > When does the series $\sum_{n=0}^\infty \frac{x^n}{3^n}$ converge?
1. Solving for power series will pretty much start with the ratio test. 1. Solving for any power series usually starts with the ratio test.
1. Create a ratio with $n + 1$ and $n$.
$$ \frac{x^{n+1}}{3^{n+1}} \cdot \frac{3^n}{x^n} $$