Determine whether the following series converges. Justify your answer.\\
$\sum_{k=0}^{\infty} \frac{9k}{\sqrt[3]{k^3 + 4}}$
Select the correct choice below and fill in the answer box to complete your choice.\
(Type an exact answer.)
A. The Ratio Test yields $r = \boxed{\text{ }}$ This is less than 1, so the series converges by the Ratio Test.
B. The series is a geometric series with common ratio $\boxed{\text{ }}$ This is less than 1, so the series converges by the properties of a geometric series.
C. Because $\lim_{k \to \infty} \frac{9k}{\sqrt[3]{k^3 + 4}} = \boxed{\text{ }}$, the series diverges by the Divergence Test.
D. The series is a geometric series with common ratio $\boxed{\text{ }}$ This is greater than 1, so the series diverges by the properties of a geometric series.
E. Because $\lim_{k \to \infty} \frac{9k}{\sqrt[3]{k^3 + 4}} = \boxed{\text{ }}$, the series converges by the Divergence Test.
F. The Ratio Test yields $r = \boxed{\text{ }}$ This is greater than 1, so the series diverges by the Ratio Test.
