Consider the series \displaystyle \sum_{n=1}^{\infty} \frac{2^n n!}{6 \cdot 9 \cdot 12 \cdot \cdots \cdot (3 n + 3)} . Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does not exist, type "DNE".
\lim_{n\to\infty} \left|\frac{a_{n+1}}{a_n}\right|=L
Answer: L =

Determine whether the series is* absolutely convergent, * * conditionally convergent, * or * divergent. * Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent".

Answer:
choose one
Absolutely Convergent
Conditionally Convergent
Divergent

What can you say about the series using the Ratio Test? Answer "Convergent", "Divergent", or "Inconclusive".

Answer:

Determine whether the series is

Answer:

In order to get credit for this problem all answers must be correct.