Heres the question:

Consider the following difference equation

P(n) = P(n-1) + k*P(n-1)*(A - P(n-1))

(a) Show that A - P(n) = (1 - kP(n-1))*(A - P(n-1))

I have already solved a and am just including it incase it is needed to solve b

(b) If 1-kA>0 and P(n-1)<A, show that P(n)<A

b is the one I need help with and I really dont know what to do...