Direct proof that $\sum_{n\geq 0}\frac{x^n}{n!}=\lim_{n\rightarrow\infty}(1+\frac{x}{n})^n$

Question

Is there a direct proof that $$\sum_{n\geq 0}\frac{x^n}{n!}=\lim_{n\rightarrow\infty}(1+\frac{x}{n})^n?$$

We dont know what logarithms or exponentials are.