A [[Power Series]] is a [[Series]] in the form $\huge \begin{align} \sum_{n=0}^{\infty} c_{n}x^n &= c_{0} +c_{1}x^1 +c_{2}x^2 +\cdots \end{align}$ For a given power series $\sum_{n=0}^{\infty} c_{n}(x-a)^n$, there are only 3 possibilities: - The series [[Convergent Series|Converges]] only when $x=a$ - Only values of $x$ within a [[Radius of Convergence]] will [[Convergent Series|Converge]] - The [[Series]] [[Convergent Series|Converges]] for all values of $x$ .