Real numbers/Power series/Definition

Let ${\displaystyle {}{\left(c_{n}\right)}_{n\in \mathbb {N} }}$ be a sequence of real numbers and ${\displaystyle {}x}$ another real number. Then the series

${\displaystyle \sum _{n=0}^{\infty }c_{n}x^{n}}$

is called the power series in ${\displaystyle {}x}$ for the coefficients ${\displaystyle {}{\left(c_{n}\right)}_{n\in \mathbb {N} }}$.