Pole of a function, as a geometric series

[cragar]

Homework Statement

Determine the order of the poles for the given function.
f(z)=\frac{1}{1+e^z}

Homework Equations

The Attempt at a Solution

I know if you set the denominator equal to zero
you get z=ln(-1)
But if you expand the function as a geometric series ,
1-e^{z}+e^{2z}...
I don't see how there is a pole in the geometric series expansion , there is no division by zero. [/B]

 

[vela]

You want to expand as a series consisting of powers of $z-z_0$ about the point $z_0 = i\pi$.