Compute the sum of the given series. If the series diverges, enter DNE. Use exact values.

n=3\displaystyle {\sum_{{{n}={3}}}^{\infty}} (1)n12n28n=\displaystyle \frac{{{\left(-{1}\right)}^{{{n}-{1}}}}}{{{2}^{{{n}-{2}}}{8}^{{n}}}}=