Consider the following series.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-1{)}^{n1}(n6)}{ln(n6)}$

Find the following limit$.($If the limit is infinite, enter $\text{'}\text{'}$ or $\text{'}-\text{'},$ as appropriate. If the limit does not otherwise exist, enter DNE.$)$

$\underset{n}{lim}\frac{n6}{ln(n6)}=$

Determine the convergence or divergence of the series.

converges

diverges