Prove divergence of a series I have to prove that $\frac{e^x}{x^k} \to \infty$  for $x \to \infty$ with $k \in \mathbb N$
My idea is to calculate for $R \gt 0$ an $x_r$ so that for every $ x\gt x_r$ the inequation $\frac{e^x}{x^k} \gt R$ applies.
So, I struggle with solving the equation $\frac{e^{x_r}}{x_{r}^k} = R$ for $x_r$

As $\displaystyle e^x=\sum_{r=0}^\infty\frac{x^r}{r!}$
For any finite $k\ge0,$
$$\lim_{x\to\infty}\frac{e^x}{x^k}\to\infty$$
