you can't sum like that. If you condition, then you would need to write
for, x1 <= x2
Sigma(x1=1 to infinity) Sigma(x2=x_1 to infinity) z^x1 p(1 - p)^(x1-1) . p(1 - p)^(x2-1)
= ...
for, x2 < x1
Sigma(x1=1 to infinity) Sigma(x2=1 to x_1-1) z^x2 p(1 - p)^(x1-1) . p(1 - p)^(x2-1)
= ...