APFIVE Power Series Interval of Convergence
The power series $$\displaystyle\sum_{n=0}^{\infty} d_n (x + 3)^n$$ converges at $$x = 1$$ and diverges at $$x = 3$$. Which of the following statements must be true?
I. The series converges at $$x = 0$$.
II. The series diverges at $$x = -7$$.
III. The series diverges at $$x = 4$$.
A
$$\displaystyle I$$ only
B
$$\displaystyle I$$ and $$II$$ only
C
$$\displaystyle I$$, $$II$$, and $$III$$
D
$$\displaystyle I$$ and $$III$$ only
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