Consider power series

$\displaystyle \sum a_{n}x^n = 1 + 2x + 3x^2 + x^3 + 2x^4 + 3x^5 + x^6 ...$

in which coefficients an = 1, 2, 3, 1, 2, 3, 1 ... are periodic of period 3. Find the radius of convergence and the sum of this power series.

For the radius, is it simply a task of doing the limit test, where $\displaystyle \lim \frac{a_{n+1}x^{n+1}}{a_{n}x^n}$?