# Pole of a function, as a geometric series

1. Apr 22, 2017

### cragar

1. The problem statement, all variables and given/known data
Determine the order of the poles for the given function.
$f(z)=\frac{1}{1+e^z}$

2. Relevant equations

3. 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 dont see how there is a pole in the geometric series expansion , there is no division by zero.

2. Apr 22, 2017

### vela

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