I have the following recursive process:
$f_n(t) = e^{t-1} f_{n-1}(1-(1-p)(1-t))$
The initial condition is that $f_0(t) = 1$
I calculated that $f_1(t) = e^{t-1}$
And then I also calculated $f_2(t), f_3(t)$ and $f_4(t)$.
However, the exponential terms just keep on increasing, and I am getting higher powers with non-linear terms. I don't seem to see a pattern that can be deduced here.
Any advice on how to solve this recursion would be very helpful.