Problem $2$: $(10$ pts$)$ Consider the series

${\displaystyle \underset{n=5}{\overset{}{}}}ln(\frac{n}{n1})$

$($a$)$ Find an expression for the $N-$th partial sum

$S_N=$

$($b$)$ Is the series convergent or divergent? If it's convergent, find the sum of the series.