Understanding Recurrence in Probability: Solving for hN(1) and cNcN

[shahawn11]

Homework Statement

I have to set hN(1) = cN and solve it. Afterwards I need to conclude that 0 is recurrent if and only if qx/px = infinity

Relevant Equations

Equations are in the image below

I set hN(1)hN(1) equal to cNcN, but I'm confused on how I'd be able to solve it and because of that I was not able to conclude that 0 is recurrent when qx/px = infinity

 

[Mark44]

Homework Statement:: I have to set hN(1) = cN and solve it. Afterwards I need to conclude that 0 is recurrent if and only if qx/px = infinity
Relevant Equations:: Equations are in the image below

View attachment 257753

I set hN(1)hN(1) equal to cNcN, but I'm confused on how I'd be able to solve it and because of that I was not able to conclude that 0 is recurrent when qx/px = infinity

Start by setting $h_N(1) to$c_N##. What do you get when you do this?
It is not enough to tell us what you tried -- you need to show us what you tried.