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education/math/MATH1220 (calc II)/Sequences.md
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@@ -126,4 +126,8 @@ The error for the first $n$ terms of a sequence is less than or equal to the $(n
# Power Series # Power Series
A power series centered at $c$ is a series of the form: A power series centered at $c$ is a series of the form:
$$ \sum_{n=0}^\infty a_n(x-c)^n = a_0 + a_1(x-c) + a_2(x-c)^2 + \cdots$$ $$ \sum_{n=0}^\infty a_n(x-c)^n = a_0 + a_1(x-c) + a_2(x-c)^2 + \cdots$$
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