Determine whether the sequence converges or diverges. If it converges, please compute the Limit.

$($a$)a_n$:$=\frac{ln(n)}{ln(3n+1)}$

$($b$)a_n$:$=(1-\frac{}{n}{)}^{6n}$

$($c$)a_n$:$=\frac{n!}{5^{n+1}}$