Use the Ratio Test to determine whether the series converges absolutely or diverges.
\[
\sum_{k=1}^{\infty} \frac{k^{2}}{8^{k}}
\]
Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer in simplified form.)
A. The series diverges because $r=$
B. The series converges absolutely because $r=$
c. The Ratio Test is inconclusive because $r=$

Step 1 ：We are given the series \(\sum_{k=1}^{\infty} \frac{k^{2}}{8^{k}}\). We need to determine whether this series converges or diverges.

Step 2 ：We use the Ratio Test to determine this. The Ratio Test involves taking the limit as k approaches infinity of the absolute value of the ratio of the (k+1)th term to the kth term of the series.

Step 3 ：Let's calculate the ratio of the (k+1)th term to the kth term of the series: \(\frac{8^{k}}{8^{k+1}} \cdot \frac{(k+1)^{2}}{k^{2}}\)

Step 4 ：Simplify the ratio to get \(\frac{1}{8} \cdot \frac{(k+1)^{2}}{k^{2}}\)

Step 5 ：As k approaches infinity, the ratio simplifies to \(\frac{1}{8}\)

Step 6 ：Since this value is less than 1, the series converges absolutely according to the Ratio Test.

Step 7 ：Final Answer: The series converges absolutely because \(r=\boxed{\frac{1}{8}}\)