Say we have $$\sum_{n\ge0}a_nx^n$$
Where$\:\:a_n=\begin{cases} \Phi_n, & \text{if}\ \:n\:\:\text{even} \\ \Theta_n, & \text{if}\:\:n\:\:\text{odd} \end{cases}$
Now how do we go about finding the set of values of$\:x\:$for which the series converges?
Do we add each convergence radius if such a thing is doable?
Or, if the radii are such that$\:\underset{even}{\mathbf{R}}\subset \underset{odd}{\mathbf{R}}\:$, do we simple choose the most restrictive of the latter two?
Thanks!