$1-6.$ Determine whether the following series are convergent or divergent. Show all work and indicate the test that you use.

$($Remember for alternating series, you need to determine if it is absolutely convergent, conditionally convergent, or divergent.$)(5$

points each$)$

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{n!}{e^n}$

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{n^2+1}{n^2-4n+2}$

${\displaystyle \underset{n=1}{\overset{}{}}}(\frac{n+4}{2n+3}{)}^n$

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{cos(n)(n^2+3n)}{n^3+4n^2-8n+6}$

${\displaystyle \underset{n=1}{\overset{}{}}}ln(\frac{n+3}{n-4})$

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{3^n}{n!}$