## Generating Function Discrepancy? [closed]

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??? :)

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Hi David, perhaps your question will be closed soon, because this site is used for research level questions in Mathematics, see FAQ. In any case it seems to me reasonable question for this site: math.stackexchange.com/questions – Leandro Oct 19 2011 at 4:57
Two words: "convergence radius". en.wikipedia.org/wiki/Convergence_radius – Thierry Zell Oct 19 2011 at 5:18
You also might consult your old calculus book on the subject of convergent power series, radius of convergence, etc. – Todd Trimble Oct 19 2011 at 9:36