This question has two parts. You may open the second part after you submit correct answers to the first part.
Part 1.
\displaystyle \lim_{k \to \infty} \,
\biggl \lvert \dfrac {a_{k + 1}} {a_k}
\biggr \rvert = \lim_{k \to \infty}
= .
Part 2.

Applying the ratio test to the series

Hence

You can earn partial credit on this problem.