A power series $\sum_{n=0}^{\infty}a_{n}(x+1)^{n}$ converges at $ x = 5$. Of the following intervals, which could be the interval of convergence for this series?
A. $[-5, 5]$
B. $(-3,5)$
C. $[-8,6)$
D. $(-7, 5]$
This question is supposed to have one correct answer. A doesn't work because since the center is at $-1$, there would be no radius. B doesn't work because it diverges at 5. However, C has a radius of convergence of $7$ and D has a radius of convergence of $6$ and also converges at 5.
Would C not also be a correct answer, as 5 falls within the interval of convergence? Which is the correct answer, since both converge at 5?