Hi,
I'm new to generating functions. I think I may be missing something and would like it cleared up. This is what I assume:
A generating function is an infinite power series. Assume a sequence $$.
$G(a,z)=\sum_{i=0}^\inf(a_i*z^i)$
This is also equal to:
For the special case where all $a_i=1$, then:
$G(a,z)=\frac{1}{1-z}$
How is this?
Let's plug in 3 for z into the first formula.
$\sum_{i=0}^\inf(3^i)=\inf$
$\frac{3}{1-3}=\frac{3}{2}$
These two are not the same... How can we claim that they are? Am I missing something? Did I break math??? :)
