I tried identifying the residue

[hedipaldi]

Homework Statement

how to compute the residue of 1/(cosh(z)^n) at z=ipi/2?

Homework Equations

b]3. The Attempt at a Solution [/b]
i tried to use cosh(z)=-isinh(z-ipi/2) and taylor expansion of this.then from expansion of 1/(1+z) and some algebraic manipulations i tried identifying the residue.it didn't really worked

 

[scurty]

Sometimes it is helpful to go to the Laurent series to find the coefficient of the $c_{-1}$ term. In this case it is easier to find the order of the zero in the denominator by taking derivatives. Since there are no roots in the numerator, the order of the zero is the order of the pole.