I am having problems with the following exercise:
Given the Maclaurin series $\sum_{n=0}^{\infty} c_n x^n $ is divergent for $x=-6,8$ and convergent for $x=-4,6$. What are the possible values for the radius of convergence, $R$?
The given answer is $6$, but I don't know how to deduce this.
The center of the circle of convergence is at $x=0$ because the terms are of the form $c_n(x-0)^n$.
Divergence for $x=-6$ means $R\leq 6$ while convergence for $x=6$ means $R\geq 6$, so $\boxed{R=6}$.
Behavior at the other points doesn't matter.