Question: The following four expressions are series. Are they convergent or divergent? Please indicate the test(s) that you use to support your conclusion (Test for Divergence, Integral Test, Limit Comparison Test, Alternating Series Test, Ratio Test, Root Test).

\(\sum_{n=1}^{\infty} \frac{n}{n^{3}+4}\)

\(\sum_{n=1}^{\infty} \frac{3^{n}}{n !}\)

\(\sum_{n=1}^{\infty} \frac{(-1)^{n}}{n+2}\)

\(\sum_{n=1}^{\infty} \frac{2 \cdot 5 \cdot 8 \cdots \cdots(3 n-1)}{2^{n} n !}\)

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