Implementation of integral and infinite summation

Hello,

I am having some trouble with implementing the following equation:

The trouble is with using numerical/symbolic variables/implementation.

Can someone please write down the code to help me. Implementation would be great.

The constants for the equation are: m=1; rho=0.5; H=1; I=1877; sigma=20;

For example if N=2, then: for n=1, An=0.257,Zn-1=inf,Zn=0.4146; for n=2, An=1,Zn-1=0.4146,Zn=0.1066;

Thanks for the help.