LarCalcET$89\mathrm{.}5\mathrm{.}021.$

Consider the following series.

${\displaystyle \underset{n=1}{\overset{}{}}}sin(\frac{(2n-1)}{2})$

Rewriting the sum in the form ${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n1}{a}_n$ gives $a_n=$

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.$)$

$\underset{n}{lim}{a}_n=$

Determine the convergence or divergence of the series.

converges

diverges