\text { Consider the power series } \sum_{n=0}^{\infty} a_{n} x^{n} \text { where } a_{n+3}=a_{n} \text { for all } n \text {. Find the radius of convergence of } the power series. As well, find the sum of the power series for values of x for which the series converges. Note: by sum, this means a function that depends on a and possibly an for some values of n.