Difficult z transform with a factorial

[jti5017]

Homework Statement

find z transform of:

x[n] = (1 / n!) *u[n]

u[n] is the unit step

Homework Equations

z transform equationX(z) = Ʃ x[n] * z^-n

summation is from -∞ to +∞

The Attempt at a Solution

cancel the u[n] by changing the bounds of the summation

now it is from 0 to +∞It's at this point I'm stuck, outside of performing approximations for the factorial, I'm not sure how to proceed. Any tips?

I apologize for the lack of formatted questions, I'm still a newbie when it comes to LateX

 

[rude man]

How about e^x = 1 + x + x²/2! + ... ?