# Definition:Power Series/Real Domain

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## Definition

Let $\xi \in \R$ be a real number.

Let $\sequence {a_n}$ be a sequence in $\R$.

The series $\displaystyle \sum_{n \mathop = 0}^\infty a_n \paren {x - \xi}^n$, where $x \in \R$ is a variable, is called a power series in $x$ about the point $\xi$.