Paragraph
An infinite power series is simply an infinite sum of terms of the form \(c_nx^n\) were \(c_n\) is some constant. So we might write a power series like this:
\begin{equation*}
\sum_{k=0}^\infty c_k x^k\text{.}
\end{equation*}
or expanded like this
\begin{equation*}
c_0 + c_1x + c_2x^2 + c_3x^3 + c_4x^4 + c_5x^5 + \cdots\text{.}
\end{equation*}
in-context