The series $\displaystyle \sum_{n=0}^\infty a_n(x-2)^n$ converges conditionally at $x=-1$ and diverges at $x=7$. Which of the following could be true?
A) The series converges absolutely at $x=5$.
B) The series diverges at $x=3$.
C) The series diverges at $x=0$.
D) The series converges absolutely at $x=-2$.
We can eliminate choices B and C right away. But both A and D are also impossible. Is there a correct answer anyway?