This is is pretty simple if you've read your text at all.
I'm using [MATH]k[/MATH] instead of [MATH]x[/MATH] because it's a discrete variable.
[MATH]f_X(k) = \dfrac{1}{k!(e-1)},~k\in \mathbb{N}[/MATH]
[MATH]G(z) = E[z^k] = \sum \limits_{k=1}^\infty~f_X(k) z^k = \sum \limits_{k=1}^\infty \dfrac{z^k}{k!(e-1)}[/MATH]
Does that term on the right look familiar at all? It should. What is the Taylor series for [MATH]e^z-1[/MATH] ?
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