All you need to do is check if P(k+1) is bigger or less than P(k).
This is determined by the multiplier:
and you need to check when
because that's when the P() terms start to decrease.
I still don't see how to do it. Lets say I want to determine if P(k=0) is less than or equal to P(k=1). This would allow me to show that the function starts by increasing. However, if you plug the values in, you get and . I don't see how to determine which one is greater without knowing the values.
That being sad, I also don't know how to determine when for the same reason. It's too abstract, I don't see how you can determine it without knowing some of the values.