I have the following infinite sum of a geometric and a negative binomial distribution:
$F(x) = \sum_{i=1}^{\infty} Geom(.5, i) NBinom(.5, 3+3i, x - 3+3i)$
I've been able to simplify that down to:
$F(x) = \sum_{i=1}^{\infty} \binom{x-1}{2+3i}0.5^{(i+x)}$
Is there any way to remove the infinite sum from this?