Real numbers/Power series/Definition

Power series

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

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

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