$\tiny{206.11.02.67}\\$

$\textit{Find the function represented by:} \\

\textit{Find the interval of convergence}$

\begin{align*}\displaystyle

f_{67}(x)&=\sum_{k=0}^{\infty}

\left[\frac{(x^2+1)}{4}\right]^k \\

&=?

\end{align*}

wasn't sure about the function?