How can I show that for every $\epsilon>0$, there exists an $N\in\mathbb{N}$ such that $\left|f_n(x)-f(x)\right|=\left|\left(\frac{x}{n}+1\right)^n-e^x\right|<\epsilon$ whenever $n\geq N$ and $x\in\left[-A,A\right]$? By the way, $n\in\mathbb{N}$.
In a previous exercise, I was able to show that $f_n$ does indeed converge pointwise to $f$. However, I have been stuck for hours trying to prove uniform convergence. Would anyone lend me a hand? Thanks in advance.