Help with a product of a sum of infinite series
let me start from the general form 
$$ \sum_{ k = M}^{ N } r^{k} = \frac{r^M - r^{N+1}}{ 1 - r}$$

then if you multiply $r^k$ by a unit step $u[n]$ the above series become

$$ \sum_{ k = M}^{ N } r^{k} \cdot u[k] = \sum_{ k = 0}^{ N } r^{k} $$

As you can notice the lower index become zero, because the unit step is equal to one only if $k\geq0$, otherwise is equal to zero.

Therefore in this specific case we have $u[n+4r]$ that is equal to one if the index $n+4r$ is greater or equal to zero, then:
$$ r \geq - \frac{n}{4}$$

At this point I think that you have all the necessary information to resolve the series