Let $f_n(z) = (1-z^2/n)^n$, and let $f(z)=\operatorname{exp}(-z^2)$. I need to show that $f_n$ converges uniformly to $f$ in any closed disc.
I saw this: Uniform Convergence of an Exponential Sequence of Functions, but I'm not sure the methods used there are applicable here because we're talking about the complex plane, and the logarithm function doesn't behave nicely there.