Consider the series.

$(\frac{13}{3})+(\frac{13}{3}{)}^2+(\frac{13}{3}{)}^3+(\frac{13}{3}{)}^4+$cdots

This series can $be$ written $as$ a geometric series $in$ the form ${\displaystyle \underset{n=0}{\overset{}{}}}c{r}^n.$ Identify $c$ and $rin$ the geometric series.

$(Give$ exact answers. Use symbolic notation and fractions where needed.$)$

$r=$

Calculate the sum $of$ the series.

$(Givean$ exact answer. Use symbolic notation and fractions where needed. Enter DNE $if$ the series diverges.$)$