Finding a function that has a finite limit (or at least existence)

Question

This has to do with probability, where an expectation of a random variable I'm calculating is

$E[X_n] = n^2f(n)(1-f(n))^n$. I want to find a function $f(n)$ such that $E[X_n] \rightarrow c$ which is finite, or $c < \infty$, or even better, to find such a function such that $c \in (0,1)$.

Answer 1

Using the function $$f(n)=\frac{c}{n^2}$$ Provides a limiting value equal to $c$.