Gordon Shapiro formula, am I crazy??

Hi everyone, I'm having trouble understanding how we find the Gordon Shapiro formula. Since it's the same demonstration that EV with a constant growth rate g, I'll be working with that.
Now, EV= sum(n:0-->infinity) of [FCFF(n)]/[(1+WACC)^n] = FCFF(0) * sum(n:0-->infinity) of [(1+g)^n]/[(1+WACC)^n] ... quite logic until now I hope..
Now that's an infinite series, who only converges if 1+g1+WACC which I'll be assuming here
In that case, the series is equal to [1+g]/[WACC-g], which means that in the Gordon Shapiro formula the result should be
FCFF(0)*(1+WACC)/(WACC-g) and not simply FCFF(0)/(WACC-g) ...
What am I missing here ?? Would you please help, I've been puzzled for weeks now, and I hate to learn things without bothering to know what they mean and not understanding why they are so..

Thanks in advance.